not sure if our situations comparable, but i have had back problems for over 35 years…age 65 now. i was high flying basketball player (at least in my mind) and that’s where back problems started. then day job sitting at desk (all the while shortening hip flexors) and reduced exercise from age 22-35. weekend warrior at many different sports. then took up running and because of injuries decided triathlon would give me cross training benefits. did not do much core or proper stretching/warmup until later in life.
experience bad bike crash in 03 and that started a cascade of serious injuries to back and knees.
at age 58 or so, mri says disk bulge/degeneration. i was lucky no sciatica for the most part, just local to l4-5, s1. but when it went it hurt like the dickens and threw me out of training good while. doc says do pt, but that met with limited success. probably because pts looked an saw an old horse ready for pasture. maybe it was me trying to do too much to get back in the swing of things (already had done couple of IM races). i wanted quick fix and doc said no need for surgery but we did do a couple of injections for the facets (they got irritated i guess from loss of disc height). they did help temporarily as steriod component made me feel strong and ready to go. but after a few months back to the usual. one wrong move and here we go again. i like you thought it was the running but looking back i think it was the running complicated by all the compensatory biking i did (80% in aero) which shortened the hip flexors more and exaccerbated my anterior pelvic tilt even more which made margin of error in spine structure (discs and facets) even more critical. going to pts or chiro was just not fruitful. you can get all the information you need on the internet. the key is to as clearly define the problem (docs can’t always tell the exact problem…just educated guesses) try to find a routine that works for you and stick with it.
in my case, where anterior pelvic tilt seems to be the main culprit plus natural degeneration, working on hip extension has to be practiced daily (2X). just sitting here at computer shortens them and at night in side lying position with knees bent does same thing. so if i hit the hip extension things go well. if i get lazy, i pay for it in fairly short order.
your solution of shot, pt and chiro will all pay some dividends if doc can really, really zero in on the problem. a shot will give some pain relief for several months (maybe longer as you appear considerably younger than me). but if you don’t get to the root cause, well masking pain really not best route. to that end i would recommend you look at tom danielsons “core advantage” book. lots of good stuff there and cheap. and my breakthru was facilitated thru mobilitywod.com. specifically i do hip extenions with thick rubber bands and this website has tons of material on it. for a small subscription fee which can be just one month, you will glean tons of good pt stuff ( the guy is a doctor of PT).
i have rambled on enough. i hope that it helps. because if you don’t nip it in the bud, today it is the facets, tomorrow could be prolapse/herniation and compensatory problems in your overloaded muscles (quads,QL & erector spinae leading to trigger points), underloaded muscles like the hammys and glutes and the eventual knee and hip problems.
not very specific to you, but i hope the overall message gets you to thinking more about the solution. you know your body, your life habits, etc. the one silver lining is that you can get better. good luck.