Maximum of 1 month if the bone wasn't damaged.

The swelling isn't problematic provided it's red and doesn't become more painful with time. The swelling is necessary for rapid healing as increased blood (and thus nutrient) supply is essential for the synthesis of fibrous tissue in the process of repair. The only complication you should look out for is concurrent infection in the area which would characterise itself as discolouration (usually yellowness) and increased pain. Other than that it should be fine.

As richrd said, 3-5 weeks if no bone was exposed, you will likely need to have your fingertip desensitized so you will be able to type properly too.

However, since this happened over 2 months ago without healing I assume it was more serious and required a splint. In which case it can take up to 4 months for proper healing and swelling to go down and before you can begin living life normally again.