You can talk to a priest, but they can’t grant you absolution.
A protestant such as me believes that forgiveness flows from God to us, but we have to make sure that we are in the faith, and that includes being born again. The LDS is a tricky subject because most mainstream Christians would say that you need to have a change of mind and heart about some core tenants of the faith that we believe Jesus has revealed. The nature of man and who we are, the nature of Jesus and Who He is, the nature of God the Father, God the Holy Spirit, etc…
You may have already done this, but take all of this to God and seek Him directly. Tell Him of your struggles and sins, admit being a sinner in need of help, calling upon Him. As a protestant, the easiest way to explain this is to emphasize that forgiveness for sin is by grace, and we receive that by faithing on Jesus as He is in reality, what He has done, and as He has revealed Himself.
In comparison with Catholicism, Protestants of my ilk tend to describe our feelings of sorrow in a similar way that Catholics describe “perfect contrition.”
O my God, I am heartily sorry for having offended Thee, and I detest all my sins, because I dread the loss of heaven, and the pains of hell; but most of all because they offend Thee, my God, Who are all good and deserving of all my love. I firmly resolve, with the help of Thy grace to confess my sins, to do penance and to amend my life. Amen.
Obviously Protestants such as me wouldn’t believe we would confess to a priest, nor do penance, but rather go straight to God and rely on the fact that our sin and our punishment were laid on Jesus. You can read more about the Catholic view of perfect contrition here; ewtn.com/vexperts/showmessage_print.asp?number=370862