All the best on your recovery
@mands, I don't anticipate it will be a very long process at all.
I wouldn't sweat the NSAID's either, the evidence showing they will negatively impact healing is outdated and new evidence shows it doesn't make a significant difference. Biggest factors for healing are diet and being aggressive with physio (doing it often).
When I broke my arm and had it operated on in 2016, I can safely say the sling was the biggest ball-breaker in the process, luckily I had a surgeon who understood the needs of a physically active guy, and he advised me to take the sling off as often as I can for as long as I can. I believe muscle starts atrophying within 48hrs of immobilization and being cut open causes stiffness in itself, so the more time in the sling you can cut out, the better!
Anecdotally, I can safely say a low dose of AAS helped in the healing process too
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I would be surprised if you lost any scale weight with mild cardio and diet being maintained.
Obviously, shoulder vs a broken arm are two completely different surgeries but I thought the similarities are interesting and worth mentioning.