Of course a physical reaction to one or more certain strains and/or types of tobacco leaf could be in play here, but I'm thinking, you being a near virgin to pipe smoking and smoking a new pipe, the crux of your issue is this:
* You're smoking in a new briar pipe. The drilling is off, but that should not impact much on your tongue bite (you may want to research "pipe mud" and fix that though). A new pipe can burn a bit hot and as mentioned, sealed finishes acerbate the problem. To migigate this, see below.
* Yep, your tobacco can be the problem, or a part of it. Try drying a bowlful of the tobacco on a piece of paper or a plate until it no longer clumps together -- depending on the tobacco blend, this can take 10 minutes or several hours (in the case of highly cased aromatics, it can take a day or two).
* check your packing technique. I drop pinches in the bowl, finger tamp lightly until it feels "springy" at the top of the full bowl.
* You believe you are smoking slowly, but it's been my experience that puffers, new to the pipe, have the hardest time getting their cadence down. I suggest you sip slowly. Then slow down some more. Then still slower. Don't worry about re-lights (you shouldn't have a huge problem with re-lights anyway if you dried the tobacco properly).
*Use matches, Zippo or a soft butane lighter. Avoid torches. Take care not to burn the pipe's rim while lighting (a little saliva on the finger, wiped around the rim mitigates burning somewhat too).