You should never be asked to train beyond your limits, BUT with that said, you may not know your limits. Training should be progressive, pushing it a little bit more each week will allow you to get further in your toughness and endurance but not hurt you as bad as you're hurting now. Lower ranked/older students need to train within their limits before they can build up stamina and push it further, your teacher or instructor should not let you hurt yourself. If you're covering up the pain, well, then you're doing it to yourself, stop if you actually hurt.
Many people will tell you many different things when it comes to muscle recovery. I'm in my 30's, I've studied recovery extensively while training for the past 7 years in martial arts (I also distance run, play in a basketball leagues, etc.), here's what I like to do:
1. Stretch before and after class, hot tub helps if you got one. I cannot overstate the benefits of stretching.
2. Proper nutrition - fruits, vegetables, vitamins, etc. Eat as healthy as you can afford, search out foods built for recovery. I know quick shots of sugar after an intense work out help feed the muscles. Try nature fruit juice.
3. Massage. Foam rollers, rolling pins, significant other, where ever you can get it, this helps break up scar tissue if you've ripped or pulled anything, works just like stretching only more focused.
4. Rest. Sometimes you just need time off between strenuous activity.
5. More exercise. Try light, low impact exercises that help move and warm up the muscles that are strained, many publications and experts say exercise can help speed up this process.
Other things that may help:
- Check to make sure you're breathing properly aka baby breathing (use your stomach, not your chest), if you're not breathing correctly you could be depriving muscles of valuable O2 needed to fuel the intensity.
- Some teas and over the counter rubs help with sore aching muscles, make sure you can handle them before taking them.
Martial Arts is not easy, it can be very taxing and it usually gets harder as you go along so you need to put yourself in a position to safely expand your abilities. As you climb in age and difficulty, you need to work outside of the classroom to keep your body from falling apart.