[Question] My left wrist hurts so much after doing arm exercises like push-ups.

I did arm exercises like push-ups for a few days to build up my arm strength.
When I woke up this morning, I felt pain in my left wrist.
There is swelling on the right side of my wrist, and even the slightest movement of my thumb causes extreme pain.
The rest of my fingers move without any pain, so I can type without any problems.

I can't do any movements that involve moving my thumbs together because of the pain. When I wash my hair, it hurts too much to use my left hand, so I just wash it with one hand.
There are quite a few things that are inconvenient when trying to do something without using your thumb.

I think it was strained because my weight was placed on my wrist while exercising.
Even if I put on a patch, it doesn't help relieve the swelling and pain.
I'm worried if it's just muscle pain or something like hay fever.
Should I go to the hospital in this case? What can I do at home?