A rough guess would be that the bounding box for your "bullet" is large enough that when fired horizontally it is colliding with objects and being destroyed immediately, but that wouldn't explain why you don't have that problem when facing left.
You're going to have to post your code, and some details about how your game is organised, for anyone to figure it out. Or do a link to the game files through something like dropbox or onedrive etc.
I'd take a look but don't use GMS 2, so at least for me you'd have to export it as GMS 1 (I think - definitely had some troubles loading GMS 2 files)