No, abortion is not considered an unforgivable sin. God loves you. He sent His Son to die for you. Through Jesus' blood there is forgiveness of sins. I John 1:9 reads, "If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from ALL unrighteousness." We need to pray to God, confess the sin and then ask for forgiveness through Jesus' sacrifice. God will faithfully forgive us and even cleanse us. That's God's word.
But perhaps you are concerned about I John 5:16, "There is a sin unto death: I do not say that he shall pray for it." What is this sin? Hebrews 6:4-6 teaches that if a person becomes a Christian and then denounces Jesus' sacrifice, he cannot be saved again. Salvation is only through Jesus, "Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved." (Acts 4:12) We can never say we don't need Jesus.
What are these sinners like? They have hard hearts. They are not sorry for their sins, but they REFUSE to repent. "For it is impossible for those (Christians)…if they shall fall away, to renew them again unto repentance…" (Hebrews 6:4-6). So, if a person is repentant, then that's proof she has NOT committed a sin unto death. She needs to believe I John 1:9. God will forgive her.
"The Lord is nigh unto them that are of a broken heart; and saveth such as be of a contrite spirit." "Deliver me from bloodguiltiness, O God, thou God of my salvation: and my tongue shall sing aloud of thy righteousness…The sacrifices of God are a broken spirit: a broken and a contrite heart, O God, thou wilt not despise." "For thus saith the high and lofty One that inhabiteth eternity, whose name is Holy; I dwell in the high and holy place, with him also that is of a contrite and humble spirit, to revive the spirit of the humble, and to revive the heart of the contrite ones." "For the Father Himself loveth you…" Psalms 34:18, 51:14, 15, 17, Isaiah 57:15, John 16:26.
Sometimes our hearts are so heavy, that even when we believe our sins are forgiven, we can't seem to shake the sadness. Our mind reviews our sins and our griefs over and over again. If you feel so burdened, it may be a good idea to see a Christian counselor. A good Christian counselor can help you work through your loss and find peace. Jesus promised to give us His peace, "Peace I leave with you, my peace I give unto you…let not your heart be troubled…" John 14:27. Our prayers are with you…