You can claim back from both your health insurer and on PAYE online.
Claim back from Quinn first: send your receipts into them after your next renewal and when they've assessed your claim, they'll send you back a statement of how the claim was assessed and how much you're getting back.
Then, using the PAYE online system, you can claim 20% of whatever Quinn doesn't cover, as tax relief on medical expenses. You don't need to send in the receipts, but hold onto Quinn's claims statement as they may query it at some stage in the future.
I can't recall what Quinn's deadline is for submitting out-patient receipts, but it will be in their rules book if you want to look it up. The tax relief is currently available for up to 4 years.
By the by, this thread is probably better off in either the Taxation or Insurance forums (fora?). If you want to move the thread, I think you can use the Thread Tools button above your first post to do so.