My veins are too small to donate blood- can I do anything about this?

Today I went to give blood, and I planned it 2 months ago, but they turned me down because my veins are too small. I was and still am really upset I even cried because I just really want to help someone and I'm disappointed in myself! I think it may be because I'm 17, 5'2 but I weight 8 stone and my dress size is a UK 10, US 6, so if I put on any more weight I'd be too heavy, but strangely my arms are really skinny! Do you think perhaps a doctor would be able to figure something out so I can donate? Or is there any way to help make my veins a bit bigger? Please help me I really want to help people and just give blood!