As you are able to raise your arm and rotate it, you can rule out tendon damage.
As the pain is more severe when you tilt your head, the pain may be radiating from problems in the neck
Apply a heat pack to the painful area and wear a scarf to keep your neck warm. Also keep away from any draughts.
Make an appointment to see your doctor to get the correct diagnosis or imaging and for specific physiotherapy for your particular problem.
I'm sorry to read that your Rotator Cuff is problematic again. We all know how pain, especially when chronic can disrupt our lives.
Rotator Cuff repair surgery can sometimes be iffy. There are a lot of factors that come into play. Success often depends on the severity of the tear, the surgeon preforming it and what degree of activity your lifestyle demands from your shoulder.
Rotator cuff repair surgery for a tear from a sudden injury works best if it is done within a few weeks of the injury. Unfortunately repairs of very large tears - or repairs on weak or frayed tissue are not always successful. They don't "hold" as well.
As always Remar has offered some good suggestions. Only imaging will provide you with correct answers. Your SX (symptoms) may not be from the actual Rotator Cuff itself - but from the surrounding structures. Imaging will reveal the source.
Please consult your medical provider. In the meantime I'd avoid activities that increase your pain - but don't quit using it. A frozen shoulder can be difficult if not impossible to repair completely. NSAID(s) may be helpful in reducing pain and inflammation. If the area swells you may want to consider applying ice.
I wish you the best and hope you'll share with us what you find out. I hope something we've said has been helpful. I'll look forward to hearing from you again soon.