Hello,
This makes me wonder, if you're used to smoking a lot of cigarettes, are you trying to smoke a pipe too much? You might not be able to smoke all day long yet without scorching your tongue. It's a different kind of mouth-stamina. Either way, on top of the other recommendations to your mechanics, you might need to give it a break for a few days as it sounds like your mouth is getting irritated which smoking will likely only worsen.
A problem may be that this is such a shitty tobacco. It could be a body chemistry thing, if it's not a problem with mechanics. Captain Black with all the crap they put in their tobacco might not agree with you and may give you a bad reaction.
As others are saying, tamp. And stop doing that. Unless you want burn your tongue so bad you stop smoking entirely, which wouldn't be a bad thing either. Take a few puffs of your pipe when it's empty--then before you light a bowl take a few unlit puffs to be sure that the draw is nearly the same after filling. It should never feel tight--the tobacco expands a good deal when the flame hits and may be cutting off the airflow.
Good luck! Keep us updated!