It is absolutely possible for moisturizer to make acne worse. You've probably heard the term "non-comedogenic" in advertisements for various skin products, and that means that the product is not supposed to cause zits, aka comedones. Here is a page with a more detailed explanation and a handy chart of common ingredients for reference. Additionally, www.cosdna.com allows you to input the name of an ingredient and returns the comedogenicity and irritancy ratings. I haven't used it extensively, but it has matched up with the Fulton scale on each search I've done so far.
However, comedogenicity ratings are definitely not to be taken as gospel. Acne is highly individual and multifactorial, so there is no way to derive a universally accurate scale of ingredients that will or will not cause acne. It can certainly be a helpful tool, but if it were that simple, no one would have long-term acne! ;)
Moisturizer can also cause skin issues via sensitivity or allergy to any of the ingredients. I have very sensitive skin and am allergic to just about everything, so that happens to me all the time and I've just thrown in the towel and started making my own moisturizer. You should talk to your doctor about your individual situation (especially about concurrent use of the two treatments), but the answer to your question in general is yes. Moisturizer can cause all kinds of problems, but to figure out which ones you're experiencing, you'll need to be examined.
Good luck... I hope your skin feels better soon!