My skin is pretty sensitive too. I always try lip plumpers on the side of my hand to see how it reacts. (If it irritates my hand I know it will for sure on my lips since they have a greater sensitivity).
I could feel it tingle on my hand, but not so much that I think it would be full on burn my lips. If you have ever played with Too Face Lip Injection Extreme it's definitely not as strong as that.
I believe it is sold in both Ulta and Sephora so if there's a store near you, you can try it out there.