Well I am not a vet but that doesn't sound normal to me!
For sure this is something you want to have checked out by your vet, and probably sooner rather than later. My guess would be that you are feeling something else, but there is no way to know for sure without a proper examination. Hopefully it's nothing serious and just the way your cat's body is but it's best not to take any chances with these sorts of things!
Good luck and let us know what the vet says- I'd be really curious!