Would it be a good idea for me to get a painkiller injection (for something wrong with the shoulder joint and not the tricep) right before my game to limit the pain?

No: This approach is almost never appropriate. We see this kind of thing glamorized in professional athletes. What is not well shown are the consequences of this kind of approach. Professional athletes use their bodies in unsustainable ways because of the significant short-term monetary gains. It is a questionable approach, even in that context. In the absence of the reward, it is highly ill-advised.