I recommend that you see your primary care doctor
about this. They can examine the sore area at the base of your thumb and determine what type of injury
this is exactly and what to do about it.
By far the most common type of injury in the place that you describe is something called tendonitis. This is an inflammation of the tendons that connect to the base of the thumb and that help to move it. These tendons can often become inflamed with repetitive actions, such as typing on a computer keyboard.
Usually a case of tendonitis can be managed with anti inflammatory medications prescribed by your primary care doctor. Sometimes your doctor may also recommend ice to reduce inflammation. In more severe cases, they may want to splint your wrist to minimize strain on the thumb.
Of course, they will also likely advise you to avoid any actions that further cause damage or strain, which might include avoiding using the computer for a while.
Start by going to see your doctor at your earliest convenience. They will be able to help you decide how bad the inflammation is and what steps you need to take to get back to normal as quickly as possible.