I just reread your question and saw something I didn't think about the first time I read it. You have lower back pain and the doc said to ride a more upright setting bike. Odd, I had fusion on my very last two vertebrates, I found riding a standard road bike more comfortable than a more upright riding position like my mountain bikes. I asked the doc about this and he agreed, that due to leaning over and riding it's stretching that area of the bike and not only relieving lower pain but it also relieves the sciatic nerve pain I also had issues with. This came from my orthopedic surgeon not a quackopractor.
Even my physical therapist said the same thing which is why my first sessions were about sitting in chair and leaning forward at my waist and touch the floor with my hands and holding so as to stretch that area.
I'm no doctor, but I know people with back issues, those with mid to upper back issues have problems riding a road bike but not a more upright bike, those with lower have had it reversed like me. So maybe you have more of a middle back issue and down as low as mine? Think about what your physical therapist has you doing, if they are having you do stretches similar to what I said then a standard road bike will help you and not hurt you. You can always try riding a regular road bike and see how it feels. No bike, upright or road style, will be comfortable for back issues the longer the miles go, this is because of the jarring that being sent up your butt and into your spine, but personally I just grin and bear it, but I don't get to that point to around the 75 mile mark, it use to painful much sooner than that but as the healing time progressed the mileage I can ride without pain went higher, hopefully this will happen for you, if it's degenerative disk issue you're dealing with then it will get worse until you stop it surgically.
Taking epidural steroid shots to remove the pain only prolongs the eventuality of surgery, plus the shots will deteriorate things even faster then nothing will work, even surgery recovery will take a lot longer if ever get to a decent level of pain because of the damage the shots did. My surgeon gave me one shot, later asked how it went, I said not much changed, at that point he said he would not give me another shot even though he could give me up to three, but to preserve the bones it would be better to do the surgery with good bone material that will remain good for the rest of my life, plus the repair would heal faster.
I don't like those guys you're seeing, you need to see a orthopedic doctor/surgeon that specializes in backs and has a good reputation. If you live in a small city that doesn't have that expertise than go to a large city nearby that will have a doctor with that expertise.