I think the injections can help but I never had much luck with them. I never had more than a few days of pain relief. I suspect the help they offer depends upon how significant your degenerative changes are. If they aren't very significant than the injections might help.
I found that if I did more exercises than I was asked to do during PT it would cause flare-ups a day or two after my session. Pay attention to how you feel while doing your physical therapy. I you are feeling stressed, stop or let your therapist know. They might be able to do some changes that will help you.
Did the insurance company explain their reason for denying the injection? You could have the request resubmitted or appeal the denial and ask for the diagnosis codes that were the reason for the denial. Your doctor's office could have used incorrect diagnosis codes when requesting the injection. I know you are probably feeling hopeless when it comes to pain relief. Don't give into that feeling. There is hope; you might need to try some other approaches. I did a lot of walking in a local pool with warm water (about 82 degrees). That will help strengthen the muscles around your lower spine and in the pelvic area. I would walk for 1/2 hour, do some other water exercises and then sit in a hot tub for about 10 minutes. Check with hotels near you to see if they rent out time in their pool. The heat will help your muscles relax and will give you some pain relief in the process.
With a degenerative spine, you will probably always have some level of pain, but you can learn to help control it. You just have to allow yourself time to discover what works for you.