WCA, bit bias as I'm a physio. Accupunture may make you feel better, but at the end of the day you probably have two naff shoulders that need some serious stabilisation to prevent it happening again. I like to think most physio's are holistic as we do chiropractor type manipulations-if needed, accupucture-if needed and proper rehab based treatment. I'm a big biker/ski-ier and had more than my fair share of stacks, including knackered shoulder. Shoulders need some hard work to get them back to full strength. Full range of moment may be quick, but proper strengthening takes a load a time.
Get a decent physio and take time with rehab. Private may cost more, but make sure they are worth it, otherwise NHS you could get an 20 year qualified physio for free! Good luck