Is having major bruising and jaw tightness after wisdom teeth removal normal?

Could be: Wisdom tooth removal is a surgical procedure. The more complex the surgery, the more post-operative complications possible. Return to your oral surgeon for evaluation.

Sometimes: Check back with your dentist if it does not start to improve in a week. The jaw tightness may need some stretching to get it back to normal.. If it does not improve within 2 to 3 weeks and is left alone the limited opening can become permanent.

Yes but: Yes, tightness normal, "major bruising" not. See oral surgeon to make sure you're within normal limits for your case.