You can, because you have the ability to, but it doesn't mean you will or you should. Most people don't feel like swimming with the flu. If you have the flu you should be resting in bed to allow your body to have all the energy it needs to fight the flu and heal yourself.
If you have a fever from the flu, swimming in a lake or cool pool can mask the symptoms and make you feel temporarily better, but that will only be temporary and the exercise will make you feel worse once you get out. If you get in a heated pool, it could make your fever worse. Don't use a hot tub when you have a fever.
If you are in a lake or pool without chemicals to kill germs, you could be shedding viruses that might live long enough to infect someone else in the same water. Don't swim with others when you are sick with any infectious disease.
Being out in public if you are still sick risks giving it to other people whether they are in the water with you or not. Stay home.
So, the bottom line is you can but you should not.
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According to the Centers for Disease Control and Prevention, there is no evidence that the Novel H1N1 flu virus can be transmitted by swimming in treated pools:
Can the new H1N1 flu virus be spread through water in swimming pools, spas, water parks, interactive fountains, and other treated recreational water venues?
Influenza viruses infect the human upper respiratory tract. There has never been a documented case of influenza virus infection associated with water exposure. Recreational water that has been treated at CDC recommended disinfectant levels does not likely pose a risk for transmission of influenza viruses. No research has been completed on the susceptibility of the H1N1 influenza virus to chlorine and other disinfectants used in Swimming Pools, spas, water parks, interactive fountains, and other treated recreational venues. However, recent studies have demonstrated that free chlorine levels recommended by CDC (1-3 parts per million [ppm or mg/L] for pools and 2-5 ppm for spas) are adequate to disinfect avian influenza A (H5N1) virus. It is likely that other influenza viruses such as novel H1N1 virus would also be similarly disinfected by chlorine. Can H1N1 influenza virus be spread at recreational water venues outside of the water?
Yes, recreational water venues are no different than any other group setting. The spread of this novel H1N1 flu is thought to be happening in the same way that seasonal flu spreads. Flu viruses are spread mainly from person to person through coughing or sneezing of people with influenza. Sometimes people may become infected by touching something with flu viruses on it and then touching their mouth or nose.
So if you are not the one sick, there should be no problem in treated pools.
If you are the one sick, you can swim, because you have the ability to, but it doesn't mean you will or you should. Most people don't feel like swimming when ill with the flu. If you have the flu you should be resting in bed to allow your body to have all the energy it needs to fight the flu and heal yourself.
If you have a fever from the flu, swimming in a lake or cool pool can mask the symptoms and make you feel temporarily better, but that will only be temporary and the exercise will make you feel worse once you get out. If you get in a heated pool, it could make your fever worse. Don't use a hot tub when you have a fever.
If you are in a lake or pool without chemicals to kill germs, you could be shedding viruses that might live long enough to infect someone else in the same water. Don't swim with others when you are sick with any infectious disease.
Being out in public if you are still sick risks giving it to other people whether they are in the water with you or not. Stay home, rest and drink plenty of fluids.
You can, because you have the ability to, but it doesn't mean you will or you should. Most people don't feel like swimming with the flu. If you have the flu you should be resting in bed to allow your body to have all the energy it needs to fight the flu and heal yourself.
If you have a fever from the flu, swimming in a lake or cool pool can mask the symptoms and make you feel temporarily better, but that will only be temporary and the exercise will make you feel worse once you get out. If you get in a heated pool, it could make your fever worse. Don't use a hot tub when you have a fever.
If you are in a lake or pool without chemicals to kill germs, you could be shedding viruses that might live long enough to infect someone else in the same water. Don't swim with others when you are sick with any infectious disease.
Being out in public if you are still sick risks giving it to other people whether they are in the water with you or not. Stay home.
So, the bottom line is you can but you should not.
Ask your doctor.
Another answer
If, you are not throwing up you need liquids replaced in your body. If, your not hungry drink chicken broth.