The medical term is "medial epicondylitis". This "tendoniopathy" involves the attachment of the wrist pronators (palm down position) and flexors at the medial (inside) epicondyle (the bony protuberance of the humerus). The injury is similar to almost any other "over use" injury with redness, swelling and the development of scar tissue noted over time pathologically.
More than 90% of patients respond to conservative measures such as: restrictive splinting (hampers motion in those planes which cause symptoms), NSAIDS, "band therapy" (much like what your describing) OP, and/or physical therapy. IMO almost ALL patients respond to what is called RICE therapy (REST, ICE, COMPRESSION and ELEVATION) with time.
Nevertheless some patients do NOT respond in a timely fashion and may prefer a more aggressive approach. The latter can effectively accomplished with corticosteroid ingestions.
These injections are essentially VOID of morbidity IF PERFORMED CORRECTLY (direct injection of the TENDON and JOINT must be avoided) which is ENTIRELY different than the injection of corticosteroids into large joints.. The latter may certainly create complications since their primary mechanism involves the SOFTENING of articular cartilage!
Finally on RARE occasions some patients, professional athletes in particular, may require surgical resection and reattachment of the scarred tissue, which over may limit ROM over time itself.
I would suggest you obtain a formal diagnosis since there are 3-4 other overlap diagnoses such as: ulnar nerve entrapment, bursitis, and ulnar collateral ligament disruption which should be entertained at presentation.
Best
jim