Thank you, Everyone, for your helpful suggestions about Silk and her allergies. I got a comment from Ann about how garlic might be dangerous for horses, so I went on-line and investigated it. I found a good article on EquiSearch that made me decide that I wouldn't risk trying it. So, an extra big hug to Ann for alerting me!
It's so interesting how easy it is to upset the delicate balance of your horse's health. I did consider other possibilities with Silk's itching, like something in the pasture or in the hay. I soaked their hay for a while to see if it helped. In the end, I really do believe it's the gnats. She had a similar reaction to the blackflies last fall. I see the little buggers flying around her, so I am pretty convinced that they are the problem.
I'm also very wary of giving my horses any herbs or supplements without consulting a vet. A couple of winters ago, the girls started chewing on the wood fence in the corral. I fed them this product from a very well-known equine company that was supposed to control the problem. It worked, but I had a terrifying experience with Silk. One morning, she collapsed on top of me when I opened the door to her stall to feed her. It was a nightmare that was never really resolved. The vet came out and Silk's heartbeat was muffled. We rushed her to the equine hospital and did all kinds of tests. The closest answer the vet could come up with was that this supplement had a lot of electrolytes in it and might have thrown her electrolyte balance off.
The lesson it taught me is that a call to my vets is free and always welcomed by them. I vowed never to give the horses anything without checking with them first. I am grateful that Ann reminded me of that before I added anything new to their menu.