I think I know what you've done!
In the NHS app, if (after correctly entering your email address) you accidentally click on 'Forgotten your password' (rather than in the actual password field), that should get a message sent to your email address to enable you to reset your password.
My guess is that you've tapped there by mistake but, for some reason, the reset code hasn't arrived in your inbox. It shouldn't matter though, as your existing password should still work if you simply try to access the NHS app again.