It can be the ultraviolet rays in the sunshine that cause your red eyes. The sunshine on the beach, as we all know, is usually very strong, and if your eyes are exposed to the sun for a long time without any measures of sunscreening, such as wearing a pair of sunglasses, it would do great harm to your eyes. The ultraviolet rays can be very harmful to the eyes of human beings, leading to permanent damages in the conjunctiva, retina, cornea, crystalline lenses, and so on and so forth. And according to your description, it may be conjunctivitis in your eyes, which refers to the inflammation of the conjunctiva, usually coming along with eye itching or dry eyes. You can try using some eye drops such as sodium cromoglycate eye drops to apply on your eyes as to ease the uncomfortable conditions. In addition, you had better buy a pair of sunglasses to prevent the sunlights from directly affecting your eyes when you are in the open on sunny day. Sunglasses with polarized lenses are better, and the dark brown and deep green colors are the best. Besides, you can also take in some cod-liver oil before sunbathing, and drink much water after it. If the condition of your eyes is very serious, you should not go to the beach again, and go to the doctor's for medical treatment as soon as possible in case of worse conditions.