Fitness

Take the time to rest that group of muscles. Focus on lower body or other exercises that don't cause you pain or discomfort. The easiest way to have a chronic issue is by not letting it heal. You can always do light weight or body weight only once it starts to feel better to check on progress.

Its better to take a week off than do long term damage. I can't say what the issue is vecause I am not a Doctor and I'm not there in person, so take it with a grain of salt. You know your body and should make the call thats right for you.

It's always a good idea to err on the side of caution with an injury. Better to take a week or two off and be able to jump back into things where you left off than to end up with a chronic issue because you keep exacerbating the injury.

Front delt isn't the worst spot, but your shoulders are involved as a minor muscle group for most upper body. If you are determined to try to do your normal sets, make sure to keep the weights light and really pay attention to what your body is telling you. If it hurts any more than a minor ache/soreness, you should stop.

I've been told that as long as there's pain that shouldn't be there, don't do that until the pain is gone. I'd still move the affected muscles a bit to see if it hurts but don't overdo it. Use smaller weights or even without weights and see if the situation improves in a few days or so.