If you made the bows from a stave and didn't violate any growth rings on the back, then the bows should be okay, if tillered properly.
On the other hand, if you made the bows from a board or accidentally cut through a growth ring or two, then the bow(s)' integrity might be in jeopardy. IF that's the case, then a backing would be appropriate here. If it was me, I would go with rawhide. You might try getting one or two of those gigantic rawhide dog bones you find at Wal-Mart or any pet shop. Or, you can go to 3 Rivers' or Kustom King's website and order rawhide from them. If using the dog bone rawhide, take it and soak it in water to soften it up real good and do a search in the bowyers' section on here for backing bows and go from there.
Again, if the bows are tillered properly and were made form a stave with a solid growth ring on the back, the bows should last many, many years.