A girl I like was saying she struggled with school in the past.
I tried to show I cared for her by saying
"It must be difficult for you back then.
It must have been hard and difficult for you.".

She got angry with what I said and said she could definitely type faster than me.
I am not entirely sure how by caring for her she could suddenly be angry at me.
I assume I word my responses badly and made her think I thought she is not intelligent so struggled at school.

Around few weeks have passed now.
She would sometimes say things to hurt me (relating to my intelligence).

Should I apologize to her?

Or

Would apologizing make the situation worst?

I see nothing wrong with apologizing for a misunderstanding, but be aware she may not apologize back for taking it the wrong way. In that case I leave her alone. You can never tell where things lead or how they turn out unless you give it a try.