I think that the difference is about the object of what you are good at/with. If it is a verb, you will use at. For example you are good at playing poker (not with playing poker), you are good at cooking pasta (not with cooking pasta). In general if it is a noun you will use with. For instance I could say I am not good with words, or with numbers (and not at words or at numbers). I hope it helps!

I'm really surprised with the answers to "I'm good with that." This is a slang which means you are okay with the method or what's being suggested. Example: Are you good with the small sized Coke or do you want to go with the larger one? "I'm good with the small size."

When you say "I'm good at that" that means you are doing good something, but "with that" means you have a good relation to something.

I will be ok

I been through alot