Likely causation. Try rather adding 10-15s a day to the duration of your cold shower. Some research shows cold showers after 2-2.5 minutes aren't giving you any benefits and over 10 minutes are outright dangerous (unless you are a pro-athlete in recovery).

Even if you do it for longer time, you can still catch horrible cold - I got deep sinusitis knocking me out for a month and am still have some mild symptoms (it was a combination of a bacterial infection, another virus and cold showers prior to catching it). Be careful!