What are the chances my baby will end up okay after potential measles exposure?

Unfortunately I had to take my baby to the ER today. Afterwards I find out there have been a couple exposures at the hospital over the last month. We were there for 2 hrs and so far there hasn't been an outbreak for that time but im not sure if something will come out in the future...

Coincidentally his 6 month shots are tomorrow and im looking to get the early mmr shot. What is the likelihood that him getting his shot tomorrow would protect him from a potential exposure today?