This is a common problem and one of the reasons we do not recommend the use of spray on type cleaners - they don’t work and they leave behind residues which are toxic and that attract more dirt to the area.
You are probably having an allergic reaction to the carpet cleaner you used. You should thoroughly wash your feet and put on shoes to protect you from recontact with the chemicals. If the itching or a rash persists, you should seek medical attention immediately. Don’t forget to take the carpet cleaner with you so they know what you’ve gotten into.
You will need to thoroughly clean the carpet to remove the chemical residues of the aerosol cleaner, the only way to do that will be with a hot water extraction carpet cleaning machine, the two we recommend the most are the Rug Doctor Might Pro and the Hoover SteamVac. Both of these machines do an excellent job of cleaning carpets.