A common rule is to stop working out if symptoms are below the neck (nausea, coughing up crap, etc.). So long as symptoms stay above the neck (runny nose, sore throat) you're good to workout just keep the intensity and duration less than usual until you're feeling 100%.

you've just done a 70.3, got sick and have an IM coming up....

suggestion from the peanut gallery, who's been there & done that... IM, start training or other significant effort before time, get sick, keep training, feel poorly for ages... i.e. idiot
so...
recover from the 70.3, because you've emptied your reserves and need to refill them before training and that's to say nothing for recovering from the muscle damage
recover from being sick - how can you train with any effort when your body is unwell and redirecting it's resources to it's own recovery... no wonder training is not going well
if you have to train, because that's what you "need" to do, then just roll though the motion, swim easy, just spin the bike, get extra sleep, eat really well... you know what you need to do and it's not more efforts.

what I observed when I started using power was the heartrate at the end of a structured warmup was a good indicator of how things were going to go, so if you break into a cold sweat and either have a too high or too low HR after 5 mins at your current FTP, then call it a day. For me, the poor performance would last a few more days after the overt symptoms cleared up.

Sounds like you just need to use your normal training time to do some walking and stretching, little strength work and wash some clothes. Your body will come back around quickly.