While there really isn't any true substitute for real "Brick Cheese", my only suggestions would be Muenster or Havarti, although both are a bit milder.
And Babetoo - "Brick Cheese" is a relatively mild, but yet very flavorful, cheese from Wisconsin. It gets a bit stronger with age, if it's a natural "Brick". I very fondly remember vacationing in the midwest & passing farmhouses with handpainted signs out front advertising it for sale. We never went thru Wisconsin without stopping & buying some. Some of those farmers had virtual cheese "caves" in their basements. It was incredible.
Commercially, the only place I've found it for sale is Wisconsin Cheese Mart. And in fact, I was just thinking of placing an order with them for both Brick Cheese & some of their Cheese Curds as well. While I've never ordered from them for myself before, I have sent cheese gifts from them to others & have received great reports back, which is good enough for me!
Wisconsin Cheese Mart-The World's Largest Selection of Wisconsin Cheese