Should I be concerned about the tightening feeling in my belly early in the 3rd trimester?

Tightening. Could be because of the growth of the baby. If it is like contractions it is normal to have mild contractions which is not painful in pregnancy. But if you're getting painful contractions you have to be seen by a gynecologist immediately.
Yes. Actually not a straight forward answer. It depends on whether or not the tightening is painful and how often it is occurring.