There are various reasons for itching after exercise and many of these are behavioral while others are due to more longstanding health conditions. It needs to be understood that exercising after a long gap or for the first time ever should not be intense whether you experience itching after a session or not.
Your body needs time to adjust to strain and when you press hard, it can react in strange ways that amplify into complications like itching, depending on your age as well as your physical condition. Many individuals have high levels of fitness irrespective of their age but caution should not be overlooked.
The behavioral causes of itching after exercise could be as simple as what you wear when you go out to exercise. For instance, tight-fitting exercise-wear which seems to be the trend now is not ideal for those who face the problem of itching after exercise.
This is because the tight fitting exercise-wear works as a barrier for the skin to breathe. In case you aren't aware, the health of your skin is dependent to a large extent on how well it is able to breathe. So, if your exercise-wear is of the tight variety, try out loser variations and see if there's a difference.
In case you don't wash your exercise-wear as regularly as you should, start doing it. Sweat drying up on exercise-wear can aggravate inflamed and sensitive skin to react and cause severe itching.
On a more serious note, if you happen to have skin conditions like psoriases or eczema, you need to get it checked by a skin specialist if exercise sweat can aggravate the condition and if so, what needs to be done. There could be other less likely causes due to hormonal changes in your body or something to do with your liver or your nerves. Seek medical advice in such cases.