Either of chair dips or pushups will work the triceps without having to lift your arms above shoulder height. And as compound exercises, they will actually work a much broader range of upper body muscles than exercises like shoulder presses.
But given your history of shoulder dislocations, I would recommend pushups, because it is more easy to work up to these gradually through wall pushups then incline pushups. Chair dips are a great exercise, but you can't modify them as easily.
I note your difficulties with physical therapy, but given there are a range of muscles that keep the shoulder in its socket, if you can strenghten these, then you may reduce your dislocation problems. But designing exercises to achieve this requires a knowledge of anatomy as well as exercise, which puts it fairly in a physical therapists field. If at some stage in the future you can swing a physical therapist, then it may be a good idea.
The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.
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