asher362 says:

If you’ve been pierced for two years, your tongue piercing should be healed. It is not likely to be any more vulnerable to infection than the rest of your mouth as long as you practice good oral hygine.
Removing your tongue ring right now seems like an increase in risk rather than a decrease. Trying to close an opening in your tongue while your body is fighting an infection puts the piercing at more risk for collecting germs. Having your jewelry in place allows your piercing to be cleaned by saliva and mouthwash. If it picked up any dirt/germs and then closed around it you may end up with more trouble rather than less.
I think your piercing will be fine where it is for the duration of your respiratory infection. If you’d like to remove the piercing once you’re healthy again, that shouldn’t be an issue. Just remove the jewelry and keep the area well cleaned.
As a note, many people (almost the majority) can’t remove their tongue rings for more than a few hours without them beginning to close. So if you’re going to remove the piercing, be prepared to give it up forever or have it repierced later. This speedy closing can be an advantage since it reduces the time in which debris can get into the piercing. It can be a real aggravation if you were hoping to wear the piercing again later.

DragoBlo says:

Normally, removing jewelry from an infected piercing will cause an abcess.
If you’re on antibiotics for your respiritory infection, then you will be fine.