I initially hurt my shoulder about 3 weeks ago bench pressing and doing pushups. hurts to lift objects overhead and to move arm across body and back?

Free weight injury: This is why I prefer machines. Always use a spotter when increasing reps or weights. Overuse should not have lingered three weeks. Sounds most like a cuff injury or a capsular tear like a SLAP lesion. Exam would help but an MRI would be definitive.

Shoulder Injury: This could be any number of problems.If it's more on the top of the should may be a problem to York from Radokovitch your joint.If the problem it is more in the front of the shoulder,it could be a long head of the biceps problem or labral injury. It could also be an injury to the rotator cuff or the bursa above it. At three weeks, I would have a check by a sports med physcian.