Depends on what you're sick with. If you already have the flu, there's no benefit to the vaccine anymore - you're too late. Tamiflu may help if you get it quickly enough, though. But if you have an illness that isn't related to the flu, getting the vaccine will still have the desired effect - triggering your immune system to being producing antibodies against this years flu strains.
I'm down with the flu atm. Loading up on vitamin D and C helps allot. I'm taking 5 times recommended daily on the D and about 3-5 grams of C. Make sure to spread the C throughout the day, if you take too much at once it can make you constipated (i use the pure ascorbic acid powder mixed in water or juice and sip it). So far i haven't gotten above a very low grade fever, just really lethargic and have a headache.
This regimen also works well at preventing the flu, much more so than rolling the dice with the flu shot. Whole reason the flu is prevalent this time of year, we get less sun and therefore less vitamin D. Just wished i had followed my own advice on this and i might not be sick right now.
You can get the flu shot while you have the flu. As stated, there are many different strains of the flu, and the vaccine covers more than just one. So if you are sick with strain X, you can get the shot still, so that you are covered for strains Y and Z. I was told by a nurse friend of mine that this years vaccine does cover the H1N1 strain that is so prevalent this year, but he is one of those guys that just makes up things to make himself look smart sometimes....so here's your grain of salt with that bit of info.