The multiple punctures would not make acne cysts. In my experience I have never seen acne in areas of Restylane injections. And a search in the medical literature to answer your question had no reports of hyaluronic acid fillers associated with acne.
My question is what if anything is being applied in that area? Sometimes moisturizers or creams with growth factors can produce acne. Also, the nasolabial folds are prone to rosacea and seborrheic dermatitis.
I recommend that you return to your dermatologist for an evaluation of the rash. At the moment stop using anything in the area. If you do have hormonal acne, there are also a couple of things to look at.
Stop all the milk and dairy products, as they contain hormones and contribute to acne
Discuss an anti-androgen, like spironolactone for acne control with your dermatologist. Spironolactone is not to be used in a woman who is pregnant or trying to become pregnant.
Stop any irritants to the face, because if this is rosacea, anything that warms or irritates the face will make it worse.