The quercetin has a "skin protective" effect and it should not cause this, in theory.
Where on your body is the rash? Does the rash have bumps? Is it red, itchy skin without bumps? Is it warm to the touch? Any skin peeling?
What other supplements are you taking?
The sinomenine and other ingredients in BMP have history of being potentially helpful in autoimmune diseases and reduce histamines. Getting a rash from this seems unusual - but so is the tattoo thing.
Bone morphogenic proteins are certainly big players in cell differentiation, and that gets pretty complex...so almost anything could happen. I wouldn't throw away your BMP just yet though, but I would get off of it for a while and see if the rash goes away fully. If the rash is really that bad, you should go see a doctor as well.
I'm also wondering if there may be some kind of cross-interaction with something else you are taking.