I don't think you're calculating your payments correctly--monthly mortgage payments on a $120k home on a 30-year mortgage at 3.5% (more likely your 30-year fixed rate would be above 4%, but you can get ARMs in the low/mid 3's) would be $540/month. That doesn't include your property taxes or homeowner's insurance. You're probably looking at closer to $800/month in payments.
Yes, there is plenty of risk. You're taking out another $120 in debt. There's the risk the home won't sell. The risk the home won't sell for a while (costing you an extra $800/month while you're making rent/mortgage payments on your new place). The risk you lose money when you sell (you'll have to pay 6-8% in closing costs--you likely won't have that much equity built up after just a few years of residency unless you made a large down payment, but most residents use physician loans with $0 down). The risk you decide to rent it out instead and the tenants trash the place and cost you more than the profit you made from the tenants (and from your increased equity in the home). There's also the risk you decide to do a fellowship and can't absorb the costs of selling the home.
And there are the risks mentioned above, like replacing the heater/AC, general maintenance costs, etc. Most residents don't have time to do their own work on a home.
If you buy a home, assume you'll need to spend $2000/year on maintenance/upkeep on a home in that price range and have $10k in savings (at least) set aside to cover any major problems (heater & AC replacement costs $7-$8k alone).
Bottom line is you may come out ahead vs renting (NYTimes has a good rent vs buy calculator--try googling it and enter your data), but I would only buy a home (and I did buy one) with the assumption that you'll either break even or possibly lose money on the home when all is said and done. While your monthly payment is lower with buying, you still need to factor in all those maintenance costs, closing costs, etc., that you wouldn't have with renting. And if you rent, remember you can pack up and leave with a one month's notice. With buying a home, you own that mortgage until it's paid off one way or another.
The smartest financial thing you could do is share a 2bd apartment, rent a 1bd studio apartment--or better yet, just rent a room in a house. A $120k home is not going to appreciate much while you're there, so unless you're a DIY guru, the odds are you' going to sell it for what you paid (plus or minus a few thousand dollars).