Would I tell my GP? Well....maybe. Right now I would, because I don't have a rheumy (yet), but if I had a rheumy, I would tell them rather than my GP. Simple reason being that rheumatologists see a lot more issues of people being very sick, and they're much, much, MUCH less likely to assume you're a hypochondriac if you show symptoms of multiple diseases. Hell, they should know that you're MORE likely to see symptoms. GP's, however, are harder to talk to I suppose, or be understood by. However, as long as your rheumy and your GP understand you and support you (don't make any stupid snide comments), then you should definitely tell them and ask them about it. Better to find out sooner than later, so you can be proactive about it.
By the way, congratulations on becoming a Sea Monkey!