complications are rare - if you have concerns do talk to your surgeon about it though, as that can help put your mind at rest and then at least you know what steps will be taken in the very unlikely event of a complication.
I too was self-funded (in NZ though so maybe a little different) but the price I paid included any follow up care and further hospital treatment should it be needed. My surgeon was very clear about that - there would be no unseen sneaky costs if something went wrong, so I was very pleased!
Anyway, best of luck for your op - it's such an exciting journey and well worth the $$ :)