In case of not being able to make the connection, what are the steps to be taken to get on a differnt flight?

My case is:
I fly into ORD on United Airlines 501 (landing at 6:50 a.m. at T1)
I fly out from ORD on Aeromexico 669 (taking-off at 8:45 a.m. from T5)
The travel agent I bought the tickets from: Vayama.com
The ticket "holder" :Continental Airlines (my credit card was charged to Continental) - I take a Continental flight on one leg of my my return trip.

I called Vayama: they said UA should fix it (if necessary)
I called UA - they said AM should fix it (if necessary)
I called AM - they said Continental should fix it (if necessary)

Should I also call Continental to see what they say?

The problem is UA501 landed today 55 minutes later and AM669 took-off on time.
I fly tomorrow( Dec 24). If this is happening tomorrow as well, I might miss my AM 669 flight (as I have to go from T1 to T5 by ATS, and check-in in person for AM669 - I can't check-in on line through UA).

Any advice is appreciated.

Thanks in advance