It sounds like this rash has appeared rather quickly and is causing you significant discomfort. Any time you experience these kind of changes, the best thing to do is see a physician right away for a more thorough assessment. In this case, it sounds like a dermatologist
is the best physician to see, given that your predominant complaint is one that involves the skin and it sounds like your cold is getting better. There are many different possibilities for new itching and patchy erythema or irritation such as you describe. The fact that the rash is over your joints suggests that there might possibly be an underlying systemic issue (for example, psoriatic arthritis
can have skin changes over joints with arthritic changes within the joint). However, you could also be having a post-viral exanthum that will fade over time or be reacting to an allergic stimuli in the environment (suspicious whenever a rash involves the hands). The best way to figure out what is triggering this is for you to discuss your overall health history, current medications, and current symptoms with a dermatologist who can also examine your skin right away. Hopefully he or she can also prescribe something to help with the itching.