Tanning do cause blur vision, so you'd better wear sunglasses or tanning bed goggles when you tanning.
Eyes react to strong light as this kind of symptom. Because our eyes cannot fit in strong light for too long, then both pupil and crystalline lens change their size to fit the strong light. Once you get back to normal light, your pupil and crystalline lens cannot swift that soon, then blurred vision occur.
If you don't wear the protected goggles during your tanning, you will find that your eyes may easily get red. The eyes may be dry easily. The unstable eye pressure will cause your eyes to have the blurry vision. You'd better use some eye drops with anti-inflammation to make the eyes see clearly. In addition, you could use the warm compress at home to make the eyes feel comfortable.
Well, it seems that there is something wrong with your eyes. Actually, it would generate some side effects on your body if you go to tan for much too long. For example, your vision would be affected without a pair of quality sunglasses, and your skin would have some problems. Anyway, try not to do that again, and you could relieve your blurred vision by taking some rest and eye drops. If the situation looks bad, you gotta visit a doctor before it is too late.