I tore my rotator cuff this spring (good arm) and so faced some challenges in travelling solo about a month later. (I travelled a week after the injury - an anniversary trip - but my husband was with me so that was easier.)
The other point in the travel process you'll likely find quite challenging is security screening, because of the need (depending on whether) to take off/put on coats/sweaters, heave things onto the conveyor belt, take off shoes, etc.
I decided to check my 22" suitcase and travelled with just a large, lightweight purse with long shoulder straps. Luckily, I was travelling in late spring, and so when I got the airport I packed my lightweight jacket into my suitcase and checked it. I wore shoes that were easy to take off and put on one-handed.
Luckily, I didn't encounter any power-tripping security staff. The only tricky part was when I was asked to CDG to step aside for a quick body pat down and they wanted me to raise my arms to shoulder level. I had to explain (in French - what's the word for "shoulder" again?) that I couldn't raise one arm because of an injury. At that point, the security staff member became quite solicitous and treated me very gently.
The only other problem I had was that, with one shoulder out of commission and one wearing a shoulder bag, I was a little unsteady on my feet (e.g. on the bus at LHR between terminals) and needed a little extra personal space because I didn't want to bump into anyone. If I had it to do over again, I would have converted the pashmina that I packed in my purse into a sling for the trip through the airport. I could have used the support of the sling - and it might have been a clue that I needed a little time and some extra personal space.