Yes, you can get private moulds for about £80 I think including fitting.
However the NHS should provide alternative IF the user is not getting on with the standard mould, you just might have to argue with them about it and show that they're causing pain, discomfort and squealing problems.
I don't use ear moulds myself (bone anchored hearing aid joy), but the word in deafland is that earmoulds have gone downhill in the last 10yrs or more. In the past audiologists used to be able to tweak them by slicing or filing them down, now they can't and the quality of the outsourcing is often poor.
As ever, the solution is to keep going back, don't take no for an answer, escalate and ask for a more senior audiologist. Don't accept long waits. Badly fitting earmoulds are an emergency as if you get an injury you can end up unable to wear an aid at all. You may have to refuse to leave till things are sorted.
I am failing to find an article in which a severely deaf acquaintance got buds privately and found them OK even though he's severely deaf. I've asked around to see if anyone can remember it for me.