i've limited experience with a similar complaint, that is tenosynovitis of the wrist brought on due to a combination of bad positioning of my arms + excessive typing several years ago while i was completing a thesis. rest worked well for me but the problem persisted as every time my symptoms started improving i got back to typing (rush to finish thesis) and all my progress vanished. i'd highly recommend a long period of rest, but not many of us are able do achieve this adequately.
ultimately i ended up getting a cortisone injection into the tendon sheath - great results, immediate relief and nothing has recurred since. that said, i'm careful how i position my hands/arms while typing now and tend to take regular breaks from the desk, which is a good idea regardless of any acute injury.
if you're in melbourne i can recommend a few different providers for injection therapy, otherwise speak with your GP and they may recommend someone local to you. some may recommend you talk to a sports physician but this is unnecessary as general practitioners actually handle a higher volume of cases such as this as a rule anyhow and typically have a fair bit of experience referring for soft tissue injections. obviously these injections are performed under imaging guidance, so typically the person doing the injecting will be a musculoskeletal/interventional radiologist.
best of luck!