There are a few possibilities here but, given the fact that we are getting into the winter months, I think it is likely that the showering is drying out your skin too much and causing these symptoms. People with sensitive skin often have this problem during the winter. Basically, what happens is that the hot water and the soap strip the skin's protective oils away, leading to dryness, redness, and itching.
The other possibility is that you are allergic to some soap or other beauty product that you are using. This would be likely if you have recently changed to a new product and, if so, discontinuing it should do the trick.
Some simple things that you can do at home include limiting the number of showers you take, especially with very hot water. After getting out of the shower, you should pat the skin dry and immediately apply a good skin moisturizer all over.
You should also go to see your primary care doctor
about this issue. Sometimes, in addition to simple home measure like moisturizing, it is necessary to use a steroid cream to reduce redness and itching, and your doctor can help with this.