Sounds like a cable tension issue. If you don't know how to adjust this yourself, a bike shop will do it for you in about two minutes. Alternatively, it's possible the "stop" screws on the rear mech need adjusting. Again, this is a two-minute job. Worth getting someone to show you how to do these things, they're very easy.

I'd be surprised if the problem described is a result of cross-chaining. Cross-chaining might result in noisily fouling the front mech, but is less likely to give rise to it being difficult/impossible to shift at the rear