Hello. TMJ arthralgia can be caused due to many factors and the origin of pain can either be TMJ or the muscles around our joints (muscles of mastication and neck). If the cause is due to TMJ then it might be helpful but if the pain is due to muscles then it won't be beneficial. Plus, if any other cause like improper bite has not been resolved then just the steroid injection won't be that beneficial. Though intra-articular injections into TMJ are relatively safe, the cause of your TMJ disorder should be known first before going on with the treatment.
Next Steps
It would be better to talk to your doctor and get to the know the possible cause of your TMJ arthralgia. Do discuss with your doctor about options of Arthrocentesis (lavage of TMJ) since it helps to flush out all the toxins (inflammatory mediators) built up in your joint spaces.