You are not alone.
Rapamycin, without question, re-actives my latent EBV (AKA mononucleosis). For the last eight months, I have been through cycles like the one you’re describing. My symptoms include debilitating fatigue, heaviness, sweats, feeling ick, head-pressure, brainfog.
Before I had a solution, it was so bad that I was debating whether I could continue taking rapamycin.
I am continuing to take rapamycin. 
Because I’m stubborn as hell, I’ve figured it out. With research, experimentation, and doctor support, I believe I’ve figured out how to effectively address my rapa-reactivated EBV.
With the caveat that I am still dialing the specifics of how much and when, I can tell you that I can now reliably put my reactived EBV back into latency within a day if not within hours.
My current theory is that having multiple suitable antivirals is better than one, but the right one will do it. I am currently using two antivirals: andrographis (paniculata) and valcyclovar. I aim for the lowest possible dose that does the trick.
Another antiviral I recommend trying is lomatium isolate extract. (Which I can’t take because for me it’s a sleep threat, but it’s great stuff, and I would otherwise.)
Naturally, your mileage may vary, and all bodies are different.
I’ve been waiting to post this until was certain of the specifics of my solution, but I’m close enough to that. Your post inspired me to say something now.
