agree with everyone else - you didn't humiliate yourself. It's not like you took a shit in the drinking fountain or accidentally tripped and fell onto an elderly person!
It was the P"T" who humiliated herself with her shitty attitude. I would definitely email the gym manager (assuming you can't keep your cool on the phone - I wouldn't be able to.)
I was overweight and obese for 25 odd years. I've joined several gyms and never had an experience like that. Have always just been asked "What are your goals in joining the gym?" Only if I've said "to lose weight" have they suggested weighing me.
I've only (thankfully) had one experience of semi-public fat shaming which was when I went to my doctors surgery for my contraceptive injection. I had not seen this nurse before and she insisted on putting me on the scales - which were in the waiting area - before exclaiming "Goodness me!" at the readout. She then tried to find any excuse possible to not give me my injection, which at that point I had been on for 5 years, saying "I'm sure I remember you can't have depo if your BMI is over 40", leafing through her nurses reference dictionary, the medication reference guide, seaching online and even leaving the fucking room to find a doctor to ask. Because, you know, fat people shouldn't need contraception because surely nobody should want to fuck us.
I walked home with the scalding tears of rage burning my cheeks. After giving her a look that clearly said "If you caught fire, not only would I not piss on you, but I would look for the nearest flammable substances to add to the blaze."
Don't let this miserable cowbag put you off. If it's feasible, I'd look for another gym. I've had good experiences with PureGym, Xcerise4Less and The Gym group.