What Causes Cold Followed By Cough And Swelling In The Hands?

Hi. My 18 year old son started with a typical fall cold about a week and a half ago. After a week, he developed a deeper cough, and he started to have swelling in his hands. (His history has made me think he s allergic to viruses.) He s continued with the cough and occasional swelling in his hands. He s been taking zyrtec and ibuprofen cold & sinus. Today, he woke up with swelling, and many hives, too. After taking zyrtec, it took an hour for the hives to stop multiplying and start subsiding. He insists on going to work tonight, and wants to wait until Monday to see a doctor. Can this wait? (We tried 2 urgent care centers, but live near the coast of eastern central FL, where everything is still closed and many facilities are still without power!)