Yes, tanning will cause the eye damages if you do not wear the sunglasses to protect the eyes. Your eyes will get red and dry easily. Your eyes may also get infection which you need to pay attention to. After tanning, you'd better use the eye drops with anti-inflammation to release the symptom and make your eyes get comfortable.
Over time tanning can cause skin cancer and serious eye damage. It's been found that exposure to Ultraviolet radiation during tanning can cause serious damage to the external and internal structures of the eye and eyelids. It can cause serious eye disease, such as cataracts and macular degeneration. While, those problems can be prevented through wear sunglasses and brimmed hat during outdoor tanning.
Well, it seems that you like the beach and sea and lot. However, I should remind you that sunshine is the strongest light in the world, which is not what your eyes can bear. If you stare at the sun for much too long, it is natural you might get burned eyes, and decreased vision. Thus I suggest that you try to wear sunglasses next time. And try to consult a doctor with your problem.