im sorry you’re going through this baby. i cut up my arm pretty bad too once when i was a little older than you for similar reasons :(
the biggest risk to your arm from cutting is nerve or connective tissue damage. do you have any numbness or tingling? do you have full range of motion in your fingers and wrist? can you stretch your fingers all the way out wide and then make a fist? i know testing all this hurts, but if you’re capable of doing all that and you’re not experiencing freaky nerve pain in your hand, you’re probably going to be ok long term.
keep the wound clean and dry the best you can. you can apply vitamin e or scar cream too it when it’s more healed to reduce scaring.