DO NOT tell your docs unless you are having a real bad time/pains! Hydromorph should cut through such a few tiny sub doses anyway (you can try and ask for more too), and being honest with the docs in this case could cause them to treat you like shit. Trust me on this. Keep mum about it unless you have to speak, for you will be labeled, probably flagged forever, and quite possibly be under-medicated anyway.
I don't think that anybody can get 'flagged forever' as if there is a database out there that lists people as 'drug seekers' unless getting multiple prescriptions filled from multiple doctors . There are other systems in place that aim to prevent doctor shopping and the like, but they are prescription monitoring programs that record all the drugs that you have been prescribed and by who, so that you can't see multiple doctors for the same or similar types of drugs.
A doctor can mark down in your chart that you are an addict or drug seeker, but that chart is not universal, meaning that it's not leaving that office unless you give permission for it to be or if they refer you somewhere and send your chart over to the next doctor. If you just go to a doctor and don't say anything then you don't have to worry about that as long as your prescription history isn't problematic.
If you have been prescribed suboxone and go to a new doctor that may be considering prescribing you narcotics then it may be a problem since doctors are encouraged to search through the prescription database to make sure that you aren't being prescribed pain meds by another doctor or aren't being prescribed something like suboxone for addiction.
My suboxone doctor would type my name into the database before writing my prescription each month to make sure that I wasn't getting prescribed any benzos, subs, or pain meds from other doctors in between seeing him, and iit's becoming common practice for all doctors to do this before prescribing you scheduled drugs, if not before then definitely if they suspect that you are a drug seeker.
Most, if not all states have a prescription monitoring program in place, with some of them keeping records of all prescriptions within the last 2 years, and some states may even go back 5 years. They prune the records dating back a certain number of years, but the records can only go back as far as when the program started, meaning that although a program may keep the records for 2 years, if it was only started 1 year ago then anything before that will not show up on a search.
All that the database lists is drug name, dosage, and prescribing doctor. You only get flagged if you are doctor shopping and pharmacy records indicate this so the state will send you a letter basically telling you that they know what you're up to and if you do it again you're getting locked up. As long as you go back to just one doctor you are alright, but if you were to go back to more than 1 and try to get similar prescriptions filled then you would get arrested.