Yes, this is typical. Swelling should resolve in 2-3 days. I recommend following your Doctor's after care protocols in order to get the best results. I find this procedure is great for rejuvenation but needs to be combined with lasers, fillers, or skin tightening to get the ultimate outcomes. See an expert for a formal evaluation. Dr. Emer.
In my clinic we do the Vampire Facial a little differently. We begin by applying numbing cream to make the treatment more comfortable. Then we use a micro-needling device to create tiny little wounds in the skin. Once these micro-channels are open we apply the PRP (Platelet Rich Plasma) directly onto the skin. We do not inject the PRP. We have very good results with this treatment. Minimal swelling may last a day or two.