You have absolutley nothing to be embarrassed about, everyone develops and starts their periods at different times izzieamy. You have nothing at all to worry about. I didn't start my periods until I was 15/16 years old. Some girls don't get them until they are 18 years old. Are you able to talk to your mum about your worries?
Stop worrying this is perfectly normal! I was 15 when I started mine but my sister was nearly 17. Trust me when they do start you'll wish they hadn't! If you are getting teased at school about it just make it up and say you have. I know my sis did and only her really close friends knew the truth.