A parent with a drug addiction in addition to 'normal' aging issues is frustrating, heartbreaking and difficult--I hope it helps to know that you are not alone. My sister and I are dealing with a Mom who is an addict and just in the last few years has developed ailments related to age (hearing, memory, balance, very bad knees, arthritis, a fall w/broken arm & surgery, COPD, HBP etc.). Every since my father passed, allowing her to manage her own finances has been like walking a fine line. (She had never balanced a checkbook in her life until then!) I am not a professional, but I am a daughter, and I have a few suggestions. First, you didn't mention why your brother doesn't assist Mom with her finances, I am assuming he is unable to do this. Because you have several issues that overlap each other, you might want to find a central source who at the very least can help you coordinate the resources your Mom needs. I found the following information from the Tennessee Dept. of Human Services, I will try to insert it as a link but I am not very computer savvy, so you may have to copy and paste it (apologies ahead of time).
This page has phone numbers for the different areas in TN, depending on where your Mom lives. It is the page specifically for Adult Services. You should be able to get a social worker (not sure what they call them in TN) who deals with the elderly. This is a good starting point, whatever the social worker is not able to do themselves they will be able to direct you to someone who can help and then keep everything coordinated. The site does mention that they can help with cases of "self-neglect", which is kind of what is going on with your Mom (because no one is doing it to her). Not to state the obvious, but if you can get a handle on your Mom's medication issues, she may be able to manage her finances again (and as you pointed out, part of the shortage issue has to do with what she spends on meds). You can address that to a certain extent. While her doctors cannot give you medical info about her without her consent, that doesn't mean that you can't call them and TELL THEM what you think they need to know about your Mom (you just can't ask them any ?s). If you go through your Mom's meds, the Doctor's name and (usually) the clinic/hospital's phone # are on there. If there is no phone # for the Doctor, call the pharmacy it came from and they can at least help you get either the number or the clinic where the Doc practices. Then when you call the Doctors, be very direct with them, tell them that your Mom abuses XYZ type of medication and has X number of prescriptions for it and she only really needs one. You will also need to talk to your Mom and have her decide on a single geriatric Doctor, then notify the others who her Doctor is and have them forward any records to that Doctor. Your Mom should also be eligible through Medicare for a visiting nurse. This is someone who can help you (going forward) keep an eye on her meds and how she seems (drowsy etc.) and can check her meds to make sure she isn't "doctor shopping" again. These are just some ideas, once you get a hold of a social worker, they can give you more advice on how to proceed with your Mom's needs and supervision. While I realize that for some of the suggestions you actually need to be there (like going through her meds for the first time) much of it can be done in one trip. A lot can also be done on the phone.
Finally, keep reminding yourself that YOU ARE a GOOD DAUGHTER! Your Mother may be resistant at first and angry and may chew you out (it's happened to both my sister and myself). Keep in mind that she isn't thinking clearly and that you are absolutely doing the right thing for her, whether she realizes it nor not. God Bless you for caring about your Mom so much, I pray He makes this journey as easy for you as possible.
God Bless and