Generally speaking, exercises should not cause pain when performed with good form and not grossly overloaded. There can often be soreness post-exercise but pain during the movement is not at all expected.

Your question does request alternative exercises, but seeing as the bench press is a popular compound movement targeting the upper body, I think it may be important to identify exactly why there is pain rather than moving to a different compound or isolation exercise.

Without further info, all I could recommend is to try lower weights on the bar, or even no weight, if that results in the pain subsiding or going away. Regarding form, this Instagram video may be useful: https://www.instagram.com/reel/C-GdEHBRVm7/

Is the pain like in the front of the shoulder?

Maybe you need to work your back and rotator cuffs. Also stretch your pecs.