Have you considered consulting a doctor who specializes in sports medicine? You might be dealing with Rotator Cuff injuries, these are pretty common, and are very painful and debilitating if aggravated.
You didn't mention how much you've increased the weight you're benching now. Is it possible that you've upped the weight too much and have put a strain on the shoulder muscles? I used to have to keep reminding myself that weight training isn't a power-lifting contest--these days I keep a bunch of 1 1/2 and 3-pound weights on hand so I can increase lifting weight by little mouse-nibbles rather than getting hurt by overloading the bar and myself.
It's hard to think of a regimen that would totally replace benching, but wouldn't cause a similar strain. You might try flys, incline bench press, inclined d-bell curls, cross-cable rows. You might consider taking most of the weight off of the bar and just go through the motions of benching; do this very slowly and stop if it hurts. Increase the weight in small increments while you recover from the original injury.
The people here can probably make more specific suggestions
Go on line and look for a copy of The Seven-Minute Solution, this book has a lot of information about shoulder injuries, and specific advice for dealing with them, and better still, how to avoid them.
Are you working with free weights or on a machine?