Pushups are great for your chest, triceps and core. Work your way up to 50 in one set.
Install a chin-up bar in one of your doorways. Then you could do pull-ups (biceps, lats, delts) and chin-ups (lower lats, biceps) and hanging leg raises(obliques, lower abs). Put two chairs together and do dips, as well, for your triceps.
Invest in kettlebells or dumbbells, then you could do shoulder presses, shoulder shrugs, bicep curls, tricep extensions, front raises, dumbbell rows.... I could go on for hours. Two 25 pound dumbbells could go a LONG way, and would only cost you like 30-40$.
The perennial calisthenic exercises are for your core. Sit-ups, Planks, Side planks, crunches, reverse crunches, bicycle crunch, mountain climbers are all good for your core/abs/obliques and can be done easily, with no equipment.
HOWEVER! You claim you want to "build upper body muscle", and the best way to do this is by following a strength training regimen with progressive weight loads, while overcompensating calories burned with a high caloric intake and massive amounts of protein. People will say that exercising with your own bodyweight can be enough, but that depends on genetics, among many other things, and it could take YEARS.
If you truly want to build muscle, you'll need to invest in a car or a bus pass and a gym membership.
EDIT: I really can't think of much other than push-ups if you ONLY want to use body-weight and nothing else.