You can indeed play at least up to where it starts to make itself known to you. Then you should probably stop for awhile. "No pain, no gain" does not apply to this sort of thing!Be sure that your technique is really good while you are at it. Your teacher may be able to help you a lot there, particularly in figuring out what sort of movements tend to aggravate it.It may also be that some careful and well thought through physical therapy might help, even this long after the injury. That can be hard to find, depending on where you live, but might be something to think about at least.
A lot of piano repretoire requires rocking the wrist from side to side. Unfortunate for you.Alas, our physical limitations determine to some extent what our hobbies and occupations will be. Billions of people worldwide play football and other ball games. I can't predict where flying objects will go or where my limbs will contact them, so I am left out of this social skill.I was a complete failure at swimming lessons when young. OTOH I turned out to have excellent fine motor skills and rhythm, so piano lessons were a great success even though they were started because I had a hand injury. (fingertip cut off age 3).Your wrist injury may allow you to play less strenuous repretoire like hymns or ballads, but not the top level pieces. It depends what your goals are if you want to pursue it. Even pop music like Elton John might be too hard for you, not to mention a lot of Beethoven literature. Arthritis limits me now to about 2 hours of practice, so I can't do abolutely top level pieces anymore. But I'm age 66. If you haven't noticed, electric organ requires much less force than acoustic piano, and a flatter hand position is allowable. The literature also has less focus at the top level on number of notes played per unit of time. The involvement of the feet in playing notes adds a another complication, one where you are not now limited. Give that a thought. There is some demand for singers of pop music. One of the bands I heard at Riverstage last night employed a non-playing singer as the lead man and spokesman. Only one hand is required to hold a microphone, and no skill at movement. You just have to remember the words, have some wind and pitch skill, and a pleasing timbre to your voice. Churches also require singers and song leaders that do not play in many cases.Then there are arts, painting, drawing and sculpture. W. Churchill had some fame for his paintings besides his writing craft. Some people do needlework or ceramic arts. Maybe you are more talented in representational or abstract visual art than average.Have fun with whatever art you decide to pursue.