I considered a similar route. One thing to keep in mind though is what jobs will hire you for. I will be speaking in generalities below, note that there will be exceptions (although less often).
Pain Medicine: ACGME Pain Medicine Fellowship. You will learn interventional spine injections, ultrasound-guided procedures (more nerve blocks, less joints), +/- neuromodulation (spinal cord stimulators, DRG, PNS), +/- pumps. You see patients in pain, no matter whether they have anatomical reasons for pain (ex. acute radiculopathy) or non-anatomical reasons (chronic pain syndrome). You take all, you see all. If you are an academic, you will likely have inpatient pain consult responsibilities. Most pain departments are housed under anesthesiology departments. If you are in private practice, you will likely be in pain practice, although some are in surgical groups with orthopedic/neurosurgeons. You will have to manage pain medications, both narcotic and non-narcotic. More often your patients are older and may be difficult to manage. See the Pain Forum for more.
Sports Medicine: ACGME Sports Medicine Fellowship. You will likely learn ultrasound-guided procedures, maybe some diagnostic ultrasound, maybe some regenerative medicine. You will likely have team coverage. For practice, you will likely be (A) in an orthopedic group as their non-operative MSK guy, (B) in an academic sports medicine practice, or (C) working as a PM&R physician who also had a fellowship in Sports Medicine. Like was mentioned, true "sports only" jobs are not super common. You will see athletes, but also weekend warriors who went running and tripped and fell. To stay afloat in private practice, you will likely have to do a good amount of team coverage, which is often not paid and is extra time after work. You are more likely to have more motivated patients who truly want to get better. A lot of your patients will start off with physical therapy as your first prescription. You may or may not get spine training in your fellowship (most places do not teach spine). If you do get spine training, most likely it will be limited to mostly lumbar epidurals, SI joint injections, and facet joints. Some may incorporate MBB/RFA in lumbar spine, but less likely. Spine is not the focus of sports medicine fellowships now. As was mentioned by Dr. DJ Kennedy (Sports-trained, Spine practice) at Vanderbilt in the PM&R Interventional Podcast, if you are a sports physician who does spine, your practice will likely become more and more spine, low back pain, neck pain, etc, and less of true sports.
Spine Medicine: NASS Interventional Spine and Musculoskeletal Medicine Fellowship / Non-Accredited Pain Fellowship / Non-Accredited Spine Medicine Fellowship. None of these are ACGME so you will not be able to get an ACGME board certification outside of your primary specialty of PM&R. If you want to be in private practice, likely ACGME board will not matter. Some places like you to have "something" so some look at ABPM or ABIPP as other pain boards, but these are not accepted everywhere (check your desired state for coverage). You will learn interventional spine injections and do spine clinic. You will see very similar patients to the Pain Medicine group above, however, you will likely not see cancer pain, pediatric pain, palliative pain, or headache patients. As you would not have completed an ACGME fellowship, many (if not most) pain departments will not hire you. Most work private practice or in orthopedic groups, however, some do work in academic centers either under Orthopedics or PM&R.
Another thing to consider:
-If you want to do 1/2 and 1/2 sports and spine, that may be truly hard to do. Spine procedures come from (A) those referred to you for procedure only within your practice (which means you need to be doing enough to be competent and have others see you are competent so they refer to you) and (B) those who you see and set up for procedure (which means that you need to have a good amount of your clinic time be actual low back pain or neck pain in order to generate patients for spine procedures). Doing 2.5 days sports with ultrasound-guided injections and sports clinic, would only leave you with 2.5 days for spine. If you want to do spine procedures, you then should have probably at least 1.5 days for spine clinic and 1 day for spine procedures. That's only 1 day per week of spine procedures. Most "spine physicians" are doing more than 1 day a week of spine procedures.
My advice:
-Choose either (A) Pain Medicine, (B) Sports Medicine, or (C) Spine Medicine. Get really good at the area you choose and build that reputation for yourself.