I can feel you. Sometimes parents missunderstand the term "programming" not because they dont love you, but because they don't know exactly what it means. Being a programmer is not bad and it's hard enough i can say as is to become a doctor for example. So you don't have to fear about something. Tell your parents about how awesome is to become a programmer.
The worst that can happen is that your parents could get really embarrassed and tell you not to talk about it to the neighbours and relatives I suppose? It may really depend on the parents. What was their reaction like when they found out about your ability to read and write? If they didn't get too upset about that, I think it'll be OK to reveal your new found power to them. Just take a deep breath and you'll be fine.... and may the force be with you!
Every parents want that their child should be happy and do whatever they want rather than talking to your parents show your skills explain them how much passionate you are.Your dedication, passion, confidence will give you good result.