It has little to do with the fact it is cotton. And everything to do with how the fabric is made. I.e. how tightly wound. How the cotton was treated, and weaved. I have shirts that wrinkle easily, and shirts that hardly wrinkle at all (they are not "wrinkle proof" coated shirts).
Your best bet is take your shirt to the best dry cleaner in your area. Call them and make sure they hand press. Don't go for the "cheaper" alternative as you will then be wasting your money. Try it out if it works keep taking your shirts to them. If not, it is your shirt, and it will never change. Live with it don't worry about it. As long as it was a freshly pressed shirt when you put it on none of the wrinkles will look "wrong" or overly ugly. Shirt wrinkles are going to happen. There is also the chance your shirt sleeves are too tight.
Your best bet is take your shirt to the best dry cleaner in your area. Call them and make sure they hand press. Don't go for the "cheaper" alternative as you will then be wasting your money. Try it out if it works keep taking your shirts to them. If not, it is your shirt, and it will never change. Live with it don't worry about it. As long as it was a freshly pressed shirt when you put it on none of the wrinkles will look "wrong" or overly ugly. Shirt wrinkles are going to happen. There is also the chance your shirt sleeves are too tight.