Yes, it is really so bad for you to get some suntan lotion in your eyes which will stimulate your eyes. You should wash it out as soon as possible with clean water. Then you could use the clean cloth to dry it. You could also use the warm compress to make the eyes feel comfortable. You should be careful next time.
There are five layers in your cornea. The damage of surface layer can heal itself over time. So you just need to stop the suntan lotion from entering your inner cornea. Flush your eyes with saline water as soon as you get suntan lotion in your eyes. You will be fine soon.
Suntan is a cosmetic, which contains many chemicals. However, suntan is rarely bad for eyes if some suntan enter eyes. The best thing you can do is flush them out with clean water and blink eyes to get rid of them. The distinctive dissolving enzyme can remove something foreign matters in eyes quickly. So take it easy. If you feel burning and pain in eyes, drop some basic eye drops to alleviate them.