If the checking runs with the grain and not off of the edge there should be no problem. I usually add super glue to then.
Sounds like your wood is not quite dry enough. Sealing the back will prevent any more checking. I keep a spray can of Bullseye shellac handy and seal all wood bow backs while I am working on them, seasoned or not. You can remove it easily before finishing with an alcohol wipe down or put your finish right over the shellac. If you want to stain the back you will have to remove the shellac.