It certainly seems like you are doing your research, and the best thing to do is to discuss your concerns with your primary care doctor. The first thing that I thought of when I saw your question was also the Raynaud’s phenomenon, which occurs when blood vessels in the extremities constrict in response to cold temperatures. Although you are right that the classic Raynaud’s phenomenon usually involves the tips of the fingers turning serially white or blue before red, there are many non-classic presentations, so I don’t think that we can completely rule out Raynaud’s phenomenon just yet.
Another condition which can also sometimes causes these symptoms is cold agglutins, which are a type of antibody produced in the bloodstream, usually after specific viral or bacterial infections. When the fingers cool, these antibodies activate causing slowing of blood flow and symptoms that may be similar to those you are describing.
I would recommend that you go to see your primary care doctor about this issue as soon as you can. They will be able to perform a physical examination and help you determine whether or not further studies, such as blood tests, are indicated at this time.
In the meantime, while waiting to see your doctor, I would strongly recommend trying to avoid contact with cold things