@idlevice
De Quervains is more on the inside of the wrist/hand alongside the thumb downwards. There is a specific movement to test for it you can probably find on YouTube. It can be helped by steroid injection or ultimately operation. Wear splints until you can get it looked at properly & keep wrists rested. You can get generic wrist splints which will be better than nothing.
Long before injections or surgery - there are loads of exercises which can easily and completely resolve any wrist/arm/ shoulder based nerve conduction problems. This is just one site
www.healthline.com/health/de-quervains-tenosynovitis-exercises
Given the current circumstances it is highly unlikely you are going to be able to get a nerve conduction test or any other none urgent treatment any time soon.
As for diagnosis, if you aren't sure, google radial, medial and ulnar nerve injuries - you will find a lot of sites that have easy and clear description and diagrams that will allow you to choose the correct exercises.
There is also an "odd" piece of advice, which a physio friend told me about. A relatively under-recognised trigger is clenching or closing your hands in bed / asleep. If you can train yourself to sleep with your hand open, the back of the hand down and hanging out of the bed or on the bed, palm up, it stretches the nerves and helps them relax back into place. I know, it sounds daft. But it really helped me although it did take some effort to get it to a natural way of sleeping.
I stopped mine - which was quite bad, with regular exercises for several weeks - 3 or 4 times a day for 5 minutes or so. I still do the exercises a few times a week, especially whilst working on the computer. With dedication it is entirely possible that you could sort it before you ever get that appointment!