I have a bulging/leaking disc, (L3 I think) which was diagnosed with a MRI scan about 5 years ago. It started when DD1 was 6mths and was agony but I put up with it thinking it was normal from carrying her so much (clingy baby.) I was referred to NHS physio and spent a small fortune on a Chiropractor over a couple of years but nothing helped. [Only my opinion but I think that Chiropractor's are great for fixing sudden, acute problems but can't do much with something like this. Does wonders for DH when he "puts his back out" but not for ongoing issues iyswim.]
Anyway, eventually went private for the MRI and consultant referred me to their physio clinic where they set me up on a programme in their 'gym.' I think it's called an "active spine programme," was Bupa at the time, now Spire. It did wonders, it consisted of me going twice a week, for 12 weeks, at a pre booked time and following a programme on lots of different machines, very similar to going to a normal gym where they devise a programme to follow every time you go. You're closely monitored by your own physio who adjusts the settings/difficulty of each machine depending on how you're getting on and your pain levels. My very basic understanding is that the back pain you get with bulging/leaking discs is from the muscles in your back being tense/over compensating for the injury to your spine. With this they worked on both improving my mobility and strengthening the muscles in my core, legs and upper body to take the strain away from my lower back. It's a kind of rehab for your back. I am now mainly pain free and try to keep up the home exercises when I remember, if I get a twinge I make sure I do them religiously for a couple of weeks and the pain goes. I also go to yoga (the fast, hard kind!) and run, both things I was told by the NHS physio I'd never be able to do again.
I was very fortunate in that I get private health care through my job all costs were covered, it wasn't cheap. There were lots of people there who were paying themselves though and who found it to be worth every penny. I don't think I realised quite how miserable and grumpy I had been until I didn't have to live with the pain anymore.
I hope that's helpful and that the injection works. I was offered them as an option but went for the physio instead, I know a few who were worse than me did them both successfully. I'd be cautious of surgery though, it tends to involve fusing your spine together which reduces mobility and really should be a last resort.
Good luck and don't listen to anyone who says you need to live with it.