Exercise is actually the WORST thing that a person with MG can do, for exactly the reason that you listed. It can - quite literally - kill you.

If your muscles get tired to the point of exhaustion, there is a very real possibility that the muscles which allow your lungs to expand and contract will just stop working. If that happens, you will have to be mechanically ventilated; if that doesn't happen in time, your body will not be able to get oxygen to your brain, and in the most extreme case, you will die.

The big "myth" about exercise - for everyone, not just MGers - is that a person can somehow "build up endurance". I'm not saying that exercise is bad in general, but the fact of the matter is that a person's muscles are only ever going to work as well as their acetylcholine receptors do.

It may be that by exercising, people induce their body to release (or accept) more ACh, but that chemical is what makes everyone's muscles "work" - if your receptors can't pick it up (which is what happens in people with MG), your muscles simply aren't going to work. All the exercise in the world won't change that basic biochemical fact.

It certainly sounds like MG, so it isn't going to hurt anything to have the testing done.

At the same time, I would urge you to get tested for Celiac Disease - the vitamin deficiency that you mention, along with the fact that you have had Mono and have been "very skinny" most of your life, suggests that you might also have issues with absorption. CD is an auto-immune disease, and if you have one AI disease, you are likely to have others.

The "very healthy" diet that most of us think is healthy is pure poison to someone with CD, as their bodies are trying to actively reject anything made with wheat, barley, or rye. Once they are able to get those ingredients out of their diet, their intestines start to heal, and they start to absorb nutrients again. Many people can go years without realizing they have issues with gluten, and many people who don't test positive for CD are actually gluten-sensitive and also benefit from a GF diet.

If you do decide to get tested for CD as well, just be sure that you don't start a GF diet until after they have drawn blood for the test - otherwise, you might skew the results.