Well, it seems that there is something wrong with your eyes. Anyway, pink eyes would bring some inconveniences to your life, because sometimes it can be transmitted to other people , this is not good. If you take care of it and pay more attention, you may continue to go tanning, because pink eyes do not prevent you from go tanning. I suggest that you cure your pink eyes before going to do this.
It's better for you not to go to tanning bed, because it may aggravate your eye problem and also cause more photophobia. If you really want to go out for tanning, you must wear a pair of sunglasses which have high level of SPF to prevent sunshine from damaging your eyes. Besides, you shall not go some where with many people since pink eyes is contagious.
When you go tanning, there are a lot of UV rays, and they are very harmful to your eyes. Since you have pink eyes, if you still go tanning, the strong UV rays may aggravate your eye problem and also cause more photophobia. But if your pink eyes are not very severe, and you are eager for going tanning, you may go with wearing tanning goggles, which will help you a lot protect your eyes from the damages from UV rays.