If you are having a reaction to the badger, there are an array of new synthetic brushes that are soft, hold water and create a great lather. The Muhle black and silvertip fiber are excellent brushes. The black is very soft and still has lots of backbone. My personal favorite.

You say your razor is a Merkur non-adjustable. That covers a lot of ground. Any chance you have a model number? If not, look at the vendor sites and identify it that way. Again, some razors are not appropriate for beginners. Knowing specifically what you're using could be very helpful.