Totally totally new to trumpet world...do trumpets for left-handed people exist???

absolutly!

I met a trumpet teacher who lost her right arm.

So she played trumpet with her left hand and put her trumpet on the stump that was left of her right arm

Easy as;... just play the valves with your left hand. I have seen a left hander put a little finger support onto the Bell, but really not necessary. Finding a comfortable position for the Right Hand, around the valves may take a bit of getting used to.

If you realy want to you can take your trumpet to a repair guy and have them solder on a pinky ring for your left hand. The only problem is that if you use your left hand only the D`s and the Db will be sharp...

You could also take the trumpet in and have them remove the bell and leadpipe and reposition them opposite of their current location. The leadpipe would be somewhat lower in the new position, and the bell stem might need to be curved a bit so it could pass around the first valve slide, but it would be doable for a competent repair man. This would give you the most left handed trumpet possible without gettting one that is a mirror image of a standard trumpet.