How old are you? Why are your parents vegeterain? Are they religous? Why the fear of telling them? Sorry about the questions but it helps us to be more enlightened on the topic and better able to give advice.
If your parents finding out means that you will be exiled from the family and you disgrace them in the eyes of god, i would have to disagree with Ko and recomend that you dont tell them. Probably best not even try it until you have moved out of the house… If however you are just afraid that they will be very angry you probably should tell them. (All of this is just in my humble opinion of course).
As far as the meat eating thing goes we again would need more info, what is your current diet like (%prot,carbs,fat, total energy intake etc), how much meat will you be consuming in your new diet. If eating meat means you will be getting significantly more protein then sure, if probably will make a big difference. What is your current body composition?
I am vegetarian (lacto-ovo) and I do believe that you can make 95-98% of the progress a meat eater could. Maybe even 100% but it takes probably at least 50% more planning and thinking preparing of meals. There is less variety and apparently the food does not taste as good. But to me its worth it. I have my own reasons for being vego that i will not get into. That last 2% does not bother me that much and the extra planning etc while it is tedious at times is okay even fun problem solving at times.
Anyway, Im kinda hoping that you do try eating meat atleast for a little while. (After all I could be deluding myself and able to make 50% more progress if i ate meat but i doubt it). It would be good if you could report back to us on your progress. How much of a difference it made etc. That would be fantastic I would be very interested in your results.
Oh yeah to answer your question on whether your body will tolerate the meat I would definetly take Ko's advice and ease into it.
keep us updated!