Four weeks is a long time not to have noticed Any improvement. Maybe it's time to see a sport's doctor or physical therapist to get a definite diagnosis and advice to get things better. Good luck.
Four weeks is definitely too long for no improvement, so I absolutely agree. See a professional.
I'm not a health professional, but have had recurring problems with tendonitis and nerve compression, so here's some tidbits from personal experience.
I agree that you stay away from the piano until it gets better.
Also, examine what else might be causing these symtoms; typing, computer mouse. Try using the mouse with your left hand; it takes a week or two to get used to, but then you won't notice a difference. I say this because many ergonomic professionals suggest using your non-dominant hand to manipulate the mouse.
Is it just stiffness in the hands, or are you experiencing a numb tingling feeling in the hands? Hand pain is often just from swollen tendons, and can be managed if it is correctly treated early enough. Numbness is usually a sign of a nerve being squished by swollen tissue and is a more complicated problem. Do you feel pain at the point where the palm meets the fingers? This is a classic sign of tendonitis. Tendons are rope like tissues that run through the fingers. They are surrounded by a sheath and they slide through that sheath. When the tendons get swollen from over use they rub against the sheath and sometimes catch against the edge of the sheath. As a result your hand turns from a dextrous tool into a painful claw.
Physicians usually will treat this with an anti-inflammatory, such as Ibuprophen. This will help, but won't fix the problem. There is not alot of blood flow in tendons, so they heal very slowly. You can increase the blood flow with moist heat, and reduce swelling with cold. Some people soak their hands briefly in warm water then put an ice pack on it for 5 minutes. Some sort of massage is what will really get the blood flowing, and will remove some of the knots in the tissue. Hence, physical therapy is the best thing for hand pain. If you have insurance that covers it (or can afford it on your own), then I would suggest you push your doctor on prescribing therapy. Doctors will typically take the cheap route and use only pills, but I don't believe it is enough all by itself.
Failing that, you can also have a dear friend massage your arms and hands. And since pianists seem to have little time for finding mates, you can also do it yourself. See here:
https://www.kreinik.com/articles/news.php?newsid=32Perhaps the way you are playing the piano is to blame, others on the forum are better informed about this.
The bottom line is see a professional.
Good luck and keep your spirits up.