Why do my ears ring with my new amplifier?

Tape some tissue paper over your tweeters just to make sure it's not excessive energy in the 2-10 khz region.

Listen at lower volumes for two days. If your ears don't ring, then you have been playing it too loud, like being at a rock concert or any loud venue and coming out with ringing. This is part of incurring noise-induced hearing loss, by the way. Tinnitus can become permanent with continued exposure to loud noise.

The spl meter idea is a good one. If things are going well you might not realize how loud things are.

+1 Jafreeman,
Your listening levels are likely too high.

What Jafreeman says is absolutely true. I had a similiar situation a year or so back with my left ear only. When I sat in the room with music playing, my ear would begin a low buzzing sound. It sounded kind of like FM interstation noise.
I would leave the room and it immediately disappeared. Slowly but surely over the next month or so, it became a friend that didn't stop. Tinnitus had set in. BTW, tinnitus is a funny thing, you don't have to have hearing loss to develop it. Most times you do however. My left ear has a roll off (very sharp) above 8500hz. It doesn't really affect my hearing that much because my right ear is good on out to 15K or so.
I don't know how old you are but I would heed Jafreeman's advice. We all probably listen too loud and it doesn't affect you until one day you have a new best friend. Mine, as the ENT told me, would not be a real factor once I lived with it a while and quit listening for it. Sure enough, I only notice it when I listen for it.