What do youn mean by lymphatic acid? I’m not aware of that as a term and a google search didn’t yield anything.
You shouldn’t inject dxm. I doubt the powder you worked up is sterile, and injecting really bypasses your immune system in a way that other routes of administration don’t. If you must use a micron filter to sterilize it. The concentration you need is going to be pretty high, I would worry that an inaccurate shot could cause complications.
Avoiding first pass metabolism doesn’t avoid the metabolism which happens as the dxm circulates. It changes the ratio of dxm to dxo but it still converts in time. Looking into CYP inhibition would be a better path (and of course lower your dose of dxm by half or more if you decide to play with that.