Is it normal for my chick not to like doggy style

Different strokes for different blokes.

You are probably hitting her cervix, which is highly uncomfortable for girls (well, the majority of the time). This is quite a common occurrence with doggy-style sex.

Likely, it is especially painful for her when your thrusts become harsher. You may just want to ease up when you take her in a doggy-style position or try moving positions/angles so you aren't hitting her cervix so hard.

Yeah it can hurt sometimes

Of course. If it's painful then you should be understanding. Have her stick a coke bottle up your ass while you're on your hands and knees. Its likely going to be painful and you won't want to continue. :-) Point is...some like doggy some don't.