A useful article to read regarding the common cold and swimming.
In most cases you can swim! If your symptoms are above the neck, it's safe to exercise.
Opt out of the swimming if your chest is congested, you are wheezing or if you're suffering from an upset stomach, body aches or fatigue.
https://www.livestrong.com/article/487742-how-to-swim-while-you-have-a-cold-cough/ Source: livestrong.com