Hey Pennywise, ur about 10 cm taller than me, but your shoe size is the same as mine. You have tiny feet!

Anyways, if you want some good shoes, I'd say go with Reeboks. First of all, they're very comfortable (and durable), and secondly, Reebok stores always carry size 11 and 12, unlike Nike. Those idiots.

And about your feet burning, it could be because you're 1 foot is longer than the other. While the difference is minimal, you're exerting more pressure on the sole of your longer foot. While better quality shoes may be able to delay the effects, I'd say it's safe to say you're over exerting yourself, based on what you've said here.

Besides, running/jogging are both high impact activities, and will have adverse effects on your joints (especially your knees) in the long run. Unless you plan on becoming some sort of long distance runner, I'd suggest looking for some other form of cardio workout, like the stationary bike / rowing machine.