I agree with Porfirio that strengthening the muscles around your shoulders will reduce the risk of injury. It will also make it easier to keep you arms up. However, I also have a couple of other suggestions.

Most the most common shoulder complaint that I have heard of is with men leading women too roughly throwing them off balance. This is mainly a problem with underarm turns but can also happen with other steps. If this is the case, you need to tell your partner that he is pulling (and hurting)you.

In closed dance positions, you can help yourself learning to maintain less pressure in your connection. You do this by carrying yourself through the steps and not relying on your partner to supply all the energy to move you. This, however, is not easy and takes practice. I am always amazed how the best women dancers can (almost) make it feel like they are not there when I dance with them.

Blair