I don't believe you can necessarily get insurance to cover the cost (you would have to check with whatever insurance company you end up with - and you wouldn't need to see a physician before doing so). If insurance DOES cover the cost, most physicians should be willing to write a prescription for an OTC item. But I highly doubt insurance will cover OTCs.
However, I believe the rules for Flex Spending (FSA) is that, you can use those funds for OTC items if you have a valid prescription from a doctor. So it's not entirely covered, but you can use pre-tax dollars to pay for it. Small wins, I suppose.
I take generic Zyrtec and prescription Flonase daily - regarding price, we found Costco to have the best deals in our area on generic Zyrtec (I can't recall the price, hubs does the shopping). Flonase is covered by my insurance for $15 copay - if you're on something like this, Nasacort (triamcinolone) nasal spray just went OTC, so would probably be cheaper without insurance (not sure, as Flonase is reasonable with my insurance).
Once you do have a good supply, watch for sales (usually BOGO) on OTC items. Expiration dates are usually far out enough to have a good stash on hand.