My girlfriend isn't very affectionate and i'd just like some opinions.?

Ok so i've been dating my girlfriend for about 3 and a half months and we've seen each other about 1 to 3 times a week. I think we work well together on most fields and things have been going good but i feel like we've hit a snag. I'm a romantic guy and we've both been in relationships before for over a year. I'm 19 and she's 20 and i went for an older girl hoping she'd want to play a more equal role in the relationship. But sadly its not the case. I'm a great guy to her, i've surprised her with flowers, cooked her a romantic dinner and at the end of the night she said i was "awesome" and gave me a peck on the lips. She usually only will express her feelings for me if i do first and its only in text. She's actually made the initiative and kissed me maybe once or twice, all the other times its been me, and when we kiss its only a quick peck at the end of the night and she pulls away. Now i do like taking it slow but not this slow. One of my favorite parts in a relationship is emotional and definantely physical affection. I know she likes me but i feel i may need that in a relationship. I'd like to have made out by now or at least had a pionate kiss. I'm still a virgin and i'm not looking to have unless i know she's the right one and we've dated for longer. So i just was wondering is this normal? Do some woman just not enjoy being affectionate? I don't want to have to ask her to be more affectionate because i feel it would taint the actions, i want her to do it because she wants to and feels its right, so it's a mutual thing, rather than her just doing it to keep me around. The reason being because i've had that happen before in a relationship and it sucks. Does it make me a jerk if i ended things for those reasons? My plan is to give her a bit more time and see what happens before i decide to look elsewhere. But i would like a second opinion and any suggestions on how to bring out the affection from her. Thanks to whoever answers!