I can totally relate to this situation as I ruptured an achilles tendon while on vacation in Florida (fortunately, it was the day before we were scheduled to go home). I was flying UA at the time, going MIA-ORD-LGA to get home, in coach the entire way and had to get from the C terminal to B in ORD to catch my connection.
While I definitely feel for you, the way I see it this one is on you. The mistake was made when you booked your ticket...to think you'll make a 45 minute connection in any airport is a huge risk, broken leg or not. Since you were splurging anyway, you should have found flights giving you at least 2 hours between flights and bought your way into the PC or had a meal with the extra time.
As far as getting upset and yelling, you should know that this will get you absolutely nowhere. The fact that you fly 125K miles per year doesnt give you the right to treat people like crap - in all likelihood, that's what they'll give you in return.
BTW - the kicker to my sob story about flying home from vacation and being on crutches...when we landed at LGA my parents picked my wife and I up and informed us that they had to put our dog to sleep while we were away.