Can God forgive what I have done?
Yes. There is no sin too big for the cross. 1 John 1:9 says, "If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness." Forgiveness is received through Jesus, not earned through being good enough.
The Bible is full of people with serious pasts - Moses, David, Peter, Paul - whom God forgave and used. Shame says you have to clean yourself up first; the gospel says come as you are and let Jesus do the cleaning.
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