Hi, I'm not a doctor, but going by what I've heard from my infectious disease specialist, I wouldn't take any chances. EBV is definitely contagious by saliva/body fluids, but from what I've heard, it may also be contagious by other contact or even by air. On the plus side, if the 2-year old or newborn would get EBV, chances are it wouldn't affect them too badly since EBV is usually less severe in younger patients. Not that I would recommend TRYING to give it to them; I'm just saying I don't think you need to be avoided like the plague or anything. So again, I'm not a doctor, but that's going from some of the info. I've heard. Hope that helps, and good luck to you!
My heart goes out to you. I hope that you will make a full recovery... there are people who do.
To answer your question, I don't believe there is concrete evidence to say that you are contagious but the evidence is mounting that some pathogens (EBV probably included) are communicable. So you might not want to share your drinks with your relatives.
I hope this helps !