On pmUA it was not a problem to link your two separate flights, but with SHARES who knows what is possible. I would CALL and Speak to a res agent to see if they can help you link; if they can...great; if they can't then that should be a very clear warning sign that 1 hour is not sufficient.

You have 90% probability that you will arrive in F terminal and depart from C terminal. Assuming the res linkage can be made, keep your fingers crossed for good weather as UAX is a tertiary priority at ORD. If weather or flow control becomes an issue, which around 4-6pm is generally an issue rain, wind or shine, as ORD is over scheduled at that time. Personally, I'd try to get to ORD on an earlier flight, if it was me...but there is always a chance the stars will align and you will be fine (I'd say that for AA eagle to AA int'l too).