Bright red and on the tissue is classic for haemorrhoids -I think this is
far more likely than an ulcer
You could potentially have internal ones too - did the doctor examine you?
Just say you are constipated - there are many reasons for this.. you don't need to disclose the hydrocodone/APAP as it wouldn't cause an ulcer and you have been taking it at a safe level. You can also get OTC laxatives you could try - I don't know what is available where you live, but ideally you want a stoop softener such as PEG-3350 plus a stimulant laxative such as Senna, Docusate or Bisacodyl. Other good measures to take are make sure you are getting plenty of fibre (if you don't get much in your diet, you could suppliment it with some isphagula hulk eg Fybogel), drinking plenty of water, getting some fat in your diet especially in the form of an oil (eg olive oil) and exercising plenty.
You can also get OTC haemorrhoid preparations (eg Preparation H) which constrict the blood vessels, shrinking the haemorrhoids - creams for extermal haemorrhoids and suppositories for internal ones.
I'm sorry you're not getting any help with your pain.. have you tried non-opiate measures such as NSAIDs (naproxen, ibuprofen - can irritate your stomach and cause ulcers!! So you need to be taking some gastro-protection such as omeprazole) or gabapentin/pregabalin (Lyrica) if you have nerve pain. Physio can help too, and there are other options as well..
If you want to detox off the pain meds as you are using them to get high and want to stop then there is a lot of good info in this thread

however, if you legitimately need them for pain, and the above measures don't work, could you change doctors?