My husband is an accountant luckily so he does mine. Usually it's a bookkeeper who would add all your receipts etc. and then a tax accountant will do the actual taxes. A private accountant might accept your box of random receipts and do it for you.....but they charge by the hour! Someone at H and R probably won't be checking your numbers as they are working for a fixed fee so only file the taxes, not do the bookkeeping.
You really should try to find a tax accountant if you want the best results. My DH is not a tax accountant and says the rules change all the time. Only a tax accountant would keep up with the changes.