I've used some Simple Kind To Skin products before, and they are really good. However, I haven't had anything like that happen to me. Whilst it's not a dodgy product or anything, I would say it does sound like it's really irritating your skin. So I would stop using and switch to a product that you do know helps your skin. Is it possible for you to go speak to a doctor/dermatologist about your skin? They might be able to recommend some products that will help.
Whilst it's true that using skin products can bring out more spots, if you're feeling like it's producing a lot more & in places you wouldn't usually get them, then it's possibly an irritation. Does your skin react in other ways? e.g. burning, itching, tingling? If you go into a department store & go up to a skincare booth - ask them for some advice about the product. Whilst it's true they'll push their own products to try and get you to buy, they should still provide some useful advice and you don't have to buy their products.