I'm sorry to hear that you're having to deal with pain and difficulty walking/standing.

There are no criteria for wheelchair assistance. Nobody's going to ask for your disability id (which we don't have in the States, anyway). From what you describe, if I were you I wouldn't hesitate to ask for assistance in order to avoid having to walk and stand in line.

You can (and should) request it in conjunction with your reservation, but don't assume that the information will manage to follow you around. Ask again when you get to the airport.

Please don't worry about what people are thinking about you (in my experience, people are hardly ever thinking about anything but themselves). Consider this to be one of the ways in which you are maintaining your independence - you are arranging for the assistance you need rather than hoping that your colleagues will step into the breach.

I know (believe me!) how embarrassing and difficult it is to be seen in public the first couple of times using any sort of mobility aid, but concentrate on the freedom from pain and the fact that you are being proactive in getting your needs met and be proud of yourself.

Edited to add: tipping - you can search in this forum for tipping and find a multitude of opinions. Mine is that it's a good idea to tip the wheelchair pusher $2-5 in the US.