If anyone would know about individual immunizations for Measles, Mumps, &/or Rubella my suspicion would be 1)Childrens' Hospital, or 2)the Department of Health (where you have to go to get many immunizations that clinics don't usually carry before you travel).
What I don't know for certain, is if they are even on the market individually in this country. I DO know that in countries like Great Britain, who have healthcare for all, it's only offered as the MMR, but one can purchase the individual Measles/Mumps/Rubella shots privately. While the government debated offering the shots individually, they found by looking at other times over the past 20 years when they altered their immunization plans in the face of a public fear of "x" (egg allergies, downs syndrom, etc.) that they had a HUGE drop in the number of children getting immunized at all, versus times when they kept the program as is, but offered whatever alternative privately. <grinning> So we do know that they're MADE...perhaps a last ditch effort could be a vacation to London. Not meaning to make light of the problem, but at least we know it's possible SOMEWHERE, so hopefully it's possible here, too!
Latest numbers say that 45.7 million Americans don't have health insurance of any kind (including State medical coupons, etc.) Another 83 million are covered under State & emergency programs...so good on you for trying to get your wee one out of risk for dieing of these diseases. Soooooo many kids aren't getting their shots these days (either out of parent choice, or there being flat out no money to see the Dr.), that the risk is a lot greater of contracting one of these illnesses today then even 10 years ago. I've see measles and mumps in my travels, and they're devastating.
I wish you luck & speed in your search!!
~Z.