As someone who currently lives in Worcester (not a medical student at umass, still waiting for post interview news), I would unfortunately have to advise you not to live in boston and commute. Any way you go, the traffic is TERRIBLE in both Worcester and boston. The area where umass is (rt 9) is the worst highway in Massachusetts for both traffic and construction (in my opinion). It probably takes me about 15 minutes to get through the 1-2 mile stretch from umass down rt 9 towards Boston during traffic hours, and the traffic essentially is constant all the way down rt 9, with only a couple of ok stretches. You could bypass route 9 altogether and go the mass pike the whole way, but the nearest entrance to the mass pike is quite a distance with almost as much traffic, so even in traffic, you're probably better off staying on rt. 9 until you reach the mass pike in natick or something.
I would say that during non traffic hours you could probably do the drive in 45mins to an hour, but during traffic. . . Oof, wayyyy too long.
I imagine the commuter rail would end up being quite expensive too, but maybe you could look into that.
I will add that Worcester isn't the worst place to live. There isn't really anything to do in the city, but the surrounding towns have plenty of things to do and plenty of great restaurants. The only bad thing is the night life here, but you can always take the trip to boston, or even providence, which is actually easier to get to, and is a surprisingly awesome city with a great night life, restaurants and stuff.