There is a discussion and list of bags that do and do not fit here:
https://www.flyertalk.com/forum/unit...forcement.html
It may not be comprehensive, but it does list several TravelPro bags, so you can check for yours. As others note, you can just measure the dimensions to compare to the UA specification.
By visual estimation, I think the 757 bins, which you do not say you've tried, are the most size-restrictive, but it is really not that different. If it fits in the new 319 & 739 bins it will probably fit in all mainline aircraft bins.