Is that normal? I want to lose a little bit of weight in my tummy but more fat in other places. How do I do that?

5'2" and 120 lbs is not bad at all! As for your "tummy", do sit-ups every day and that bit will get smaller and smaller.

Don't be so hard on yourself. Your weight, based on your height is just fine. Eat better and exercise more and you can trim down some and "look and feel" more fit, but as far as height and weight goes: you're good.