Is exertional throbbing/squeezing chest pain that radiates up to jaw and sob during moderate exercise normal? had asthma as a kid. mildly overweight.

No: Pain is your bodies signal that something is amiss. I would schedule an office visit to explore the issue. While you wait, write down all the related symptoms, time of onset, aggravating factors, associated factors, etc. so you don't forget any important features during the visit. Stop the exercise routine until you are cleared to resume it.