You are absolutely correct. I am suggesting that you NOT use any type of moisturizer or cream on your skin for at least two days. Anytime you are introducing a new product to your skin, and especially after you've been applying other products/medications to the skin, you need to give the skin a break in between applications. This prepares the skin for the new product. This also gives you a more accurate assessment of the product. When you don't give the skin a break before introducing a new product, residue of the old product used on the skin taints the product effectiveness. As a result, a fair assessment of the product is not made because other foreign factors corrupt the product integrity. Having suffered with Acne in my teens and young adulthood, I learned early on about the importance of giving the skin a break in between products to prepare the skin for the switch in products.
Continue to use the soap (the one recently purchased) to clean the skin, but don't apply any moisturizer, cream, or medication to the skin for a minimum of two days. When you do apply the moisturizer, make sure that it is after the skin has been cleaned. Clean skin is essential to healthy skin.
Whole Foods Market is a national health food chain in the United States. You can visit their website to find the nearest store in your area. This would be a worthwhile visit for you because the many items I've mentioned (from hair care to skin care) are found in their stores. They also provide sample testers; so that, an individual can try the item on a small area of the skin to test for sensitivities before purchasing.
I'd rather you ask me questions than to guess at what I'm speaking; so, please don't hesitate to ask. You can personally email through this website.