Super Oily Skin After Botox and Perlane?

I can't see any reason why Botox or Perlane would make your skin oily, but since the same thing  happened when you had implant surgery it sounds like a reaction to the skin prep used to sterilize the skin before injections or surgery.

This is unusual and is probably not a result of Botox and Perlane. It could be a reaction to a topical product that has been applied recently. Did you receive numbing cream? Did you apply a new skincare product?

Perlane and Botox injected into the skin and muscles won't cause your skin to appear oily. I would consider: if anything else has changed in your skincare regime; and/or review recent topical applications. Following up with your provider will also allow them some assessment of the areas treated and you could have a discussion on the topical application they provide prior to injections.

As mentioned in several comments below, I can't think of a reason for either of these things to cause oily skin. Perhaps, your PS office has an aesthetician you can meet with to go over your change in skin.