Have you considered seeing a doctor? No one – especially a doctor will diagnose without seeing your rash and getting some medical information from you.

Yes, you can get a rash from your rabbit.  You really should see a doctor if the rash is not going away.  Animals can pass things along to humans even if they are not showing signs themselves.  Be sure to mention to your doctor that you have a pet.  Chances are it could be something else- but the sooner you find out- the sooner you can treat your bunny if the bunny has been exposed to something.

I am in no way trying to diagnose a rash- but poison ivy oils can get on a pets coat and transmit to a human without the pet every contracting poison ivy.  Also some pets can be ringworm carriers.  etc…

Honsbeek have you tried searching http://www.webmd.com to get an idea? It by no means will substitute seeing a Dr. Have you tried putting anything on it like hydrocortizone, calamine lotion, Benadryl etc.? I would book an appointment with your Dr., especially since you are talking about your eye as well.

I’m no Dr. either but there are some contagious eye infections (for example, pink eye) that can be serious and should be seen by a Dr.  It sounds to me like an allergic reaction of some type, it could be the rabbit or it could be the hay or it could be unrelated like a new soap or lotion or who knows.  You might also just book an appointment with an allergy specialist instead.  Let us know how it goes.

Edited to add that we had a member not too long ago get a rash and it was because the rabbit had mites. So you might want to take a closer look at your rabbit for signs of mites.