Well. You could always inform the teacher that if you keep up this pace you will injure yourself. And you would hate to get 90% of her salary for the rest of her life because she/he was an ass.
She likely has a general education degree and, if you keep reading this thread, knows less about the science of fitness than you will. So instead, she reads from some pre-planned generic exercise syllabus that the school gives her, simply to make sure you guys stay busy during the class period.
Tell her you injured yourself last time, and does she know any easier alternatives to the moves in the video.
Also, a yoga block will make some of the exercises easier (and safer) for you.
So if a shoulder almost feels fine when you're not touching it, but like a claw's digging into it if you give it so much of a poke, is that a good or bad pain?
If your legs aren't tired when you're running but your throat is sandpaper and it's getting hard to breathe, is that a good or bad pain?
#1 Sounds like overuse, if it feels that way the same day as the exercise. If it's three days later and it still hurts the same or worse, it's an injury. If it aches the next day or two after exercise, it's delayed onset muscle soreness.
#2 Sounds like the usual thing that happens when you breath hard for long periods of time.
Heh, the P90X has a section on this that's quote worthy:
Often, you will hear the expression "No pain, no gain" when it comes to achieving fitness results. Understand that this does not refer to the kind of pain that a trapeze artist would experience after missing the net. What it does refer to is muscle burn that is common during intense workouts. It's a GOOD pain. Let's review: missing-the-net pain, bad; muscle-burn pain during intense exercise, good!
Edit out: Biax already answered the second portion.