Short answer
Not on its own. A feeling of love or peace can be real, but it is not proof. It can be trusted only when it rests on a truth that holds up when tested. The Bible says the same. It calls the heart deceitful above all things. It tells believers to prove all things and to test every spirit. Satan deceived Adam and Eve, and he can use the very thing a person wants most, such as the longing to be loved. Jesus himself warned that many who call him Lord will be turned away. So the feeling must be checked against what Jesus taught: the Lord our God (﷾) is one Lord. Islam teaches the same: faith rests on evidence, and the feeling of worship follows from it.
Full explanation
The inner witness Christians rely on
Many Christians say they know Jesus is their Lord because they feel his presence and his love. They point to Paul, a Christian missionary of the first century. He writes that the Spirit bears witness with the believer's own spirit.
“The Spirit itself beareth witness with our spirit, that we are the children of God:”
What the Bible says about the heart
The same Bible gives the heart no such authority. The prophet Jeremiah calls it deceitful above all things. Proverbs calls the man who trusts his own heart a fool. It also warns that a way can seem right to a man and still end in death. A believer who rests his salvation on what he feels is resting it on the one thing his own scripture says cannot be trusted.
“The heart is deceitful above all things, and desperately wicked: who can know it?”
“He that trusteth in his own heart is a fool: but whoso walketh wisely, he shall be delivered.”
“There is a way which seemeth right unto a man, but the end thereof are the ways of death.”
The Bible's own command: test it
The New Testament does not tell believers to trust every spirit. It tells them to prove all things and hold fast only to what is good. It tells them to try the spirits to see whether they are of God (﷾), because many false prophets have gone out. Proverbs adds that answering a matter before hearing it is folly. A feeling that is never tested breaks all three commands.
“Prove all things; hold fast that which is good.”
“Beloved, believe not every spirit, but try the spirits whether they are of God: because many false prophets are gone out into the world.”
“He that answereth a matter before he heareth it, it is folly and shame unto him.”
The deceiver comes as a friend
Satan's method is to come in the shape a person hopes to see. Paul says he appears as an angel of light. In Genesis, Eve says the serpent beguiled her. In the Qur'an, Satan swears to Adam and Eve that he is their sincere adviser, and brings about their fall by deceit. If the thing a person most wants is love, that is where the deceiver will work. No one should think he is harder to fool than Adam and Eve were.
“And no marvel; for Satan himself is transformed into an angel of light.”
“And the man said, The woman whom thou gavest to be with me, she gave me of the tree, and I did eat. And the Lord God said unto the woman, What is this that thou hast done? And the woman said, The serpent beguiled me, and I did eat.”
“Then began Satan to whisper suggestions to them, bringing openly before their minds all their shame that was hidden from them (before): he said: "Your Lord only forbade you this tree, lest ye should become angels or such beings as live for ever." And he swore to them both, that he was their sincere adviser. So by deceit he brought about their fall: when they tasted of the tree, their shame became manifest to them, and they began to sew together the leaves of the garden over their bodies. And their Lord called unto them: "Did I not forbid you that tree, and tell you that Satan was an avowed enemy unto you?"”
Jesus' own warning
Jesus warned that not everyone who calls him Lord will enter the kingdom. Only the one who does the will of his Father will enter. He said many would come to him on that day, sure of themselves and full of works done in his name. He would tell them he never knew them. When he was asked which commandment is first, he named the oneness of God (﷾).
“Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.”
“Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works? And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.”
“And Jesus answered him, The first of all the commandments is, Hear, O Israel; The Lord our God is one Lord:”
What the Qur'an says
The Qur'an names the same danger in one question: have you seen the man who takes his own desire as his god? It says that guesswork is of no use against the truth. It answers people who were sure of their own salvation by asking for their proof. Faith in Islam rests on evidence, and the feeling of worship follows from it.
“Then seest thou such a one as takes as his god his own vain desire? Allah has, knowing (him as such), left him astray, and sealed his hearing and his heart (and understanding), and put a cover on his sight. Who, then, will guide him after Allah (has withdrawn Guidance)? Will ye not then receive admonition?”
“But most of them follow nothing but fancy: truly fancy can be of no avail against truth. Verily Allah is well aware of all that they do.”
“And they say: "None shall enter Paradise unless he be a Jew or a Christian." Those are their (vain) desires. Say: "Produce your proof if ye are truthful."”
Verse by verse
Romans 8:16 — Epistle to the Romans, chapter 8, verse 16
“The Spirit itself beareth witness with our spirit, that we are the children of God:”
Cited for
The Holy Spirit testifies inside the believer. The feeling that Jesus is Lord is that testimony, so it can be trusted.
The response
The verse does not say that every inner feeling is the Spirit. The same New Testament says to test the spirits, because false ones have gone out. John's next verse tests a spirit by what it teaches about Jesus, not by how it feels. Paul also warns that Satan appears as an angel of light. The test Jesus gave is the will of the Father and the first commandment: the Lord our God (﷾) is one Lord.
Where it lands — A feeling cannot certify itself. The Bible sends it to be tested, and the test is what Jesus taught about God (﷾).
Perspectives
Mainstream Christian
The Holy Spirit gives believers an inner assurance that they belong to God through Jesus. That assurance is part of genuine faith.
Paul writes that the Spirit bears witness with the believer's spirit that he is a child of God.
Rebuttal
Paul does write this, but he never says every inner feeling is the Spirit. John says to test the spirits, and his test is what a spirit teaches, not how it feels. Jesus' own test is the will of the Father and the first commandment: the Lord our God (﷾) is one Lord.
The Islamic perspective
A feeling is trustworthy only when it rests on truth that has been tested. Both the Bible and the Qur'an warn against following the heart or one's own desire. Jesus pointed to the oneness of God (﷾) as the first commandment.
The Bible calls the heart deceitful above all things and the man who trusts his own heart a fool.
The New Testament commands believers to prove all things and to test every spirit.
Paul says Satan appears as an angel of light.
Jesus said that many who call him Lord will be told he never knew them.
Satan brought about the fall of Adam and Eve by posing as their sincere adviser.
The Qur'an warns against taking one's own desire as a god and following guesswork instead of truth.