First, it may be right to disassociate the act from the person. I'm told that a state-of-the-art among pre-school teachers (and maybe parents), for example, is that when a young child does something wrong, you don't say:
You're a bad boy!
You reprove the act, not the person:
Don't hit people when you want something. Ask for it, use your words.
- The criticism is more specific (what not to do) and constructive (what to do instead)
- The lesson that "I am a bad boy" is not the lesson that you want the child to learn!
Similarly you might think about your friends "That was an unskillful action, hurtful", rather than, "They are bad, they hurt me" etc.
Second, if I fall of a bicycle unexpectedly and hurt myself, I've been inclined to worry about it until I work out how and why it happened -- so I can avoid repeating the mistake ... because I don't want to live in fear of its happening again for the same unknown reason.
Likewise it seems to me that a sincere and important part of an apology is something like, "I did wrong and I won't do it again."
I think that if you have any real assurance that it won't happen again, then you can afford to forgive and/or forget it (but otherwise that's more difficult).
Sometimes the hurt is of a kind where you can't get an apology: where "they" won't apologise, or the actor is a bit impersonal (maybe a war, a crime, a car crash). That kind of experience can cause what people call "post traumatic stress disorder" (PTSD) where you keep reliving the experience. PTSD is a real problem, there are therapies for it (I don't know of any Buddhist therapies) that you might want to investigate further, one of which they call "mindfulness" -- which includes being/remaining aware of what's happening now and the fact that the traumatic experience is past.
Third, if you want to forgive yourself in some way, perhaps it's good to do good things -- to intend well (e.g., kindly), and to act well when possible.
Buddhism praises both harmlessness and generosity, for example. Practising either or both of these, perhaps remembering (when you recollect your "past lives") that you have been harmless and well-intentioned, may result in your experiencing no remorse.
Fourth, you may want to compare yourself with others -- see that you're like others, better than some, only human ... not judge yourself too harshly.
The Christian prayer includes "forgive us, like we forgive others" (which sounds sensible to me).
Also when "compare yourself with others" it's good to find or recognise people who you think may be better than you, and learn from them, learn to practice as they do.