Too Much????

I'm 13. There is a girl that I am good friends with and am starting to go out with. It was just Christmas and her 13th birthday. (And we just started going out) So there were 3 kinda special events. I got her this sterling silver necklace with a pink and white cubic zirconia circle pendant on it. It was only like $20. I didn't think much of it because I really like her, but other people think that I spent too much. (I haven't actually told anyone the price) I think they think it was a lot more than that. I think that it makes me seem a little desperate. One of my teachers even poked fun at me for it. I don't want her to think (the girl, not my teacher) that I am just trying to buy her things to get me to like her. I gave it to her at the end of school two days ago and today and yesterday she wore it. I'm know she likes it, but I don't like her friends thinking I spent too much. I don't have any cles with her so I can only talk to her before and after school. Was it too much?