IANAD, so go see yours. Seriously. It could be nothing, just a circulation problem. Or it could be neurological. Only a qualified medical professional can tell you for certain.
Only a doctor could give you much of an idea. You would need, at least, someone to take a more specific history and do an exam.
Involvement of all the tips is not usually a neurologic problem because of the way the fingers are innervated. Circulation issues (Raynaud’s would be an example) can do this but are usually associated with color changes. Arthritis can do it but would give symptoms fairly specific to the DIPs (the most distal finger joints) if the pain is “at the tip.” An assortment of things can make the pads hypersensitive, and you can have problems in the pads themselves.
In short, it’s unlikely any guesses here would be anything being WAGs, and probably misleading at that.
This is worth noting again. If you have color changes (blue or white fingers), pain or feeling of cold, please see your doctor. Raynaud’s was one of the first symptoms my wife experienced before she was diagnosed with scleroderma.
I used to be a newspaper reporter and there were many occasions where I had to write several stories in one day. Even though I typed like a maniac all the time, after these several-story days my fingertips always hurt a lot.
But it always went away pretty quickly; you don’t say how long this has been bothering you – but if it continues, I’d rule out the typing.
Is the pain only when pressure is applied, or do they throb with pain with just your hands held loosely at your sides?
Have you let go of the beaker of boiling water yet? (My wife did this in Chem lab back in school, TWICE, thus disproving the adage about the burned hand teaching best.)