Pretty much all cotton clothing will eventually start to fall apart after numerous washes through the spin cycle. How many washes depends on the quality of the cotton, the quality/type of weave, and thread count. You don't have to take them to a dry cleaners, but a lot of people do(with respect to expensive shirts). Just make sure you trust the dry cleaner to not fuck up your shirt. A good cold water soak in the sink would do you just fine. Use a detergent like Woolite black to wash your shirts. And never throw them in the dryer as your shirt will shrink especially in the sleeves. If you have the room, spread them on the floor with the sleeves extended, the entire shirt wrapped between towels. Drying them with the sleeves extended out will help to prevent some of the shrinking, but cotton shirts will almost always shrink some after the first wash. Basically, the less agitation the better.
Anyways, you shouldn't really wash your shirts after each use unless you sweat like a pig or something.