Hi Annie
If the pump does its job perfectly for the kitchen and loo, but not for the shower, it certainly LOOKS like "plumbing."
Only thing is, you mentioned the shower working ok "for very short time."The shower would normally be running for longer at a time than either the kitchen tap or the loo-flush, so you should try (if you haven't already) running the kitchen tap for a longer spell.
If the pump's the problem, then it'll almost certainly play up eventually (ie when the tap has run for as long as the shower would be). If the flow at the kitchen remains smooth no matter how long you run it for, then the pump must be ok, and it's something in the plumbing.
I'm not familiar with your bathroom (!), do you have separate basin and shower taps, or a shower head that pulls out of the tap unit to fill the basin? If the latter, it's worth pulling out the shower hose as far as it will go and examining it for signs that it's been kinked when retracted - that's happened to me once.
That's about as far as I can go from experience & intelligent guesswork - anything more complicated on the plumbing side will be specific to your model, so you'll either need someone with a similar-age Bessie or a motorhome dealer.