Reading your OP, I can't stop but notice something (I highlighted it red). Correct me if I'm wrong (I'm just going by what you wrote), but you say you were angry with your family
for something you think they did to you. Did they really harm you? or did you just think they harmed you? There is a big difference.
A lot of times person A gets angry against person B, because of something person A
thinks that person B did to him/her; not because person B
actually did something wrong, but because person A
thinks person B did it.
We can convince ourselves that person B wronged us, and did something bad to us, even when they have actually not done anything of the sort, but we
think they did.
We need to be careful with this train of thought, since it can sometimes make people's lives miserable. Thinking all the time that others are wronging them, blaming others for their mistakes, etc.
It's great in your case, that you've realized that this is about you not dwelling in those feelings and moving on ("forgiving", if you will, though I'm not sure there's anything to forgive if you only thought they wronged you). It does indeed make your life happier and brighter. Congratulations.
Can I forgive? Yes. Do I forget? Eventually, since after forgiving, I usually cut those that wronged me from my life forever. So they become not even a blip on my radar.