You know getting a tan is good for your health as well as your eyes. However, everything has its modest extent, why not wearing sunglasses while sun bath? Over bright light will also damage your vision. Most of the people may know, the skin around the eyes are very subtle and delicate, it is easy to be broken. You can apply some cold towel softly on your eyes to release the pain and swollen. It will be recovered soon. You know abundant ultraviolet light will burn your skin even induce skin cancer. I suggest you to go out in the morning and do not over one hour per time. Proper prolong the time is acceptable in winter. It would boost the absorption of calcium to prevent you from rarefaction of bone. Hope you keep health in a good way!
Yes, tanning may cause your swollen eyes. If you don't wear the protected goggles when you are tanning, your eyes may easily get red. Your eyes will feel uncomfortable. You could do something to reduce the swollen eyes. You could just use the warm compress at home to make the eyes feel comfortable. In addition, you could use the eye drops to get rid of the invisible bacterium in your eyes.
It looks like your eyes have got some problems, and made your eyes look weird. From what I know, tanning would make your eyes absorb a lot of light and perhaps you didn't wear sunglasses or something, so your eyes were damaged. And in the meantime, if your eyes are allergic to strong lights, the problem would be worse. Anyway, try to consult a doctor and do not tan without proper protection.