Continue weight training with shoulder injury if pain free?

I'm having pain at the top and back (near top of deltoid to almost near my armpit) of my right shoulder when I raise my arm straight up in the air and then rotate it backwards. This only occurs at the extreme range of motion, i.e. when I really strive to stretch my arm backwards. My doctor manipulated my shoulder some this past week and does not think it is rotator cuff related. He instead thinks it's a large muscle strain of some sort (no definitive diagnosis, other than no RC injury). I've decided to lay off climbing for a few weeks, as I don't want to yard off this arm all that much at the odd angles climbing requires.

Ideally I would like to avoid losing strength during this period, but I'm worried about slowing my recovery. (I want to be 100% come September to start hanging off tools etc for ice season) I've attempted both pull ups and dips, neither of which seem to bother my shoulder any. I'm debating if I should keep doing them or not. For those of you with shoulder injuries, do you entirely cease overhead exercises until you feel better, or just avoid what feels bad and continue to work out etc?

Thanks

Best option: see a knowledgeable sports medicine professional who knows something about climbing.

Realistic option for most people: proceed with caution. Start with considerably lower volume/intensity than you normally would and slowly build up. Lots of self massage time should help as well (a lacrosse ball is your best friend). Listen to your body.