Yes it is good to sweat when you're sick and if you exercise if you're feeling able to exercise such as riding an exercise bike, jogging or even running or jogging outside in some fresh air can help your bodies immune system and help fight the flu or cold virus off.
You can't actually sweat out sickness or the flu or cold virus but when you exercise and sweat your bodies immune system gets better which means your immune system can fight that cold or flu virus off.
I do get feeling better when I exercise and even go for a jog outside in the fresh air when sick and when I'm feeling able enough to do so.
Exercising and getting your body where it's sweating can help you feel better and the sweating and exercise is good for your health and can help relieve some symptoms of the flu.
I do find that when I exercise and get sweaty that the flu seems to go away sooner and I feel much better instead of just laying around on the couch or in bed until the flu goes away.
But there's no way to actually sweat out the flu virus because for the flu to go away the virus that causes the flu has to go away or be killed off.
Sweating won't get that flu virus or even cold virus out of your body so you'll still be sick but when you sweat and exercise your boost your bodies immune system which helps to fight off that flu and cold virus.
So while you're not sweating out the flu or cold virus you are helping to kill the flu or cold virus sooner because you're boosting your bodies immune system and sweating and exercise is good for your health.