It could.......and it could take months to recover...;-)
Keep on with the pain killers and if it doesn't improve after a month........suggest (gently) that would an injection of cortisone into the joint be helpful.
I had a frozen shoulder 3 years ago. The GP didn`t want to arrange a cortisone jab (guidelines) so I waited about 6 weeks for physiotherapy. The GP printed off a list of exercises for me to do which turned out to be almost the same as the Physiotherapists advised. https://www.health.harvard.edu/shoulders/stretching-exercises-frozen-shoulder
I went for my first physio yesterday and the physiotherapist seems to think that it's arthritis related and not a frozen shoulder. She's given me some neck exercises to do and I have to go back in two weeks. I have to speak to the Dr to get some stronger pain killers as the paracetamol isn't really doing anything to kill the pain but other than that nothing has changed. She hopes to see some change within the next few weeks so we'll see how things go!