If there’s a definite temporal association between using the new product and the appearance of the itchy red rash, then yes it’s likely that it’s some form of dermatitis related to the product.
Dermatitis is also more likely if you are not getting the rash anywhere else on your body, and also have never had the rash before, nor any personal or family history of eczema/psoriasis.
The fact that the red patch comes and goes however warrants further investigation by your doctor – there may be something else in this story.
In this situation, I’d suggest for you to see a dermatologist – they are the experts in red itchy scaly patches 🙂
Cheers