Hi T.,
My son's get bumps too, but normally there is just one or two bumps not a lot of them. When he gets them We were told that they are infective taste buds. We can't explain why they get them. I was told to let them suck on a hard peice of candy like a lemon head or such or drink through a straw (kinda hard like as if they were trying to drink a thick shake through the straw)It brings them to heads and they normally disappear the following day. It does make them sore by doing this but it has always worked for us.
But your case really does sound like what the other ladies are saying the hand foot mouth. My son had that. His whole mouth was white and there was an odor to it. There is a medication that they give for this. If you suspect this please take at least one of them in. Worst case they can give you enough meds for the rest of them or at least let you know what it is.
I don't know your financial or insurance situation. But if the doctors visit can't be done, then you might want to consider taking them to you local care station or hospital. Depending on where you go if you have insurance or not they can help. If you have no insurance your kids might be entitled to the state kid health insurance program.
Hope this helps, best of luck to a speedy recovery.
L.