Anti inflammatories, rinsing with chamomile tea, application of heat. Gently stretching your fingers and palm backwards. Try not to overuse your hands. I would ask your doctor if it is okay first though.
The plantain(not banana looking fruit) is a common "weed" found in Alabama and probably many other states in the U.S is filled with anti inflammatory properties and also reduces itching. You can make a paste out of it and coconut or olive oil which both have anti inflammatory properties and apply it to the affected area. It helps my grandmothers seasonal itching and also helps with arthritis pain when rubbed on the area that hurts. Maybe not a cure all but give it a try if you can find some of the plants.
Buy some gloves from a company called Prolotex. Wear them as much as possible. I use them every time I play video games. They have really helped me and cured my CTS. They are about 50 dollars but worth every penny. You can get them with fingers or without so you can type of play video games. If your CTS is really bad get them and put them on and do not do anything for a few days. Even if you have to take off time from work. You will heal. You just need time. It is a lot better option than surgery!