Abuse is tricky. It effects each kid differently. I'd say common side effects are depression, anxiety, being overly dependent on others, attachment issues, aggression, possible personality disorders, PTSD, trouble connecting with others, trouble saying no, substance abuse, insecurity, a deep sense of loneliness, emotional problems, etc.
A common thread among abuse victims is the adamant "I'll never be like x", x being the abuser. In their efforts to be opposite to their abuser, they usually end up being more like them than they would like. This might lead to self-destructive behavior and "repeating the cycle" where they end up abusing those around them. Abuse survivors feel like things are out of their control, so they desperately try to control things (i.e. their spouse, friends, children).
Abuse victims may have commitment issues. They may be overly dependent on a spouse or a friend, or they may be extremely unfaithful and unreliable. They'll feel like shit for it, and they'll want to break that cycle, but they'll find that by themselves they can't.
Enter: solutions. Fun fact about trauma βit doesn't go away. No one person can magically "fix" your character's trauma. No one can love them better. So they can't just overcome their fears/issues because they fell in love, or they found the power of friendship. Therapy and facing their issues is one way of lessening their symptoms. Love and support can help but not cure.
That's really all I know about the subject. I'd recommend researching a lot. Google is your friend. You can probably find actual testimonies from abuse victims (I've not been physically abused, so take some of my advice with a grain of salt). Remember, though, that your character is a person outside of their trauma, their depression, their pain. Make sure to fully develop their personality. It's important that you treat such a delicate subject with respect. Good luck!