She is just too strong, I even tried the infamous urgot bot and her ult just carries her through it.

Anything with high burst, gap closers, long range or a silence/stun/suppression works well. They key is to make sure you have a way to avoid fighting Kayle when her ulti is up, or prevent her from being able to use it. You really shouldn't have any problems as urgot vs kayle provided you poke correctly.

I was playing nunu and did fine for about 15 minute

but once she farms up, i have no idea how... At least not when i was playing a non bursty bot.

Champions with Attack Speed slows work well against Kayle.

nasus or nunu however nasus is specifically a counterpick so if you don't know its coming then :/

other options are to get FH and wardens mail both

Champions that counter her are:
Nunu (Super Sustain Mode Nunu), Malphite (hardest counter), Nasus

However, this is probably blind pick, so you don't have that luxury. You pretty much have to have Frozen Heart and/or Wardens Mail/Randuins Omen. That's almost like QSS is to Malz - you don't completely gimp them, but it definitely shuts down a lot of their dps.

Champs with good burst or consistent high DPS work well, or ones that can disengage once she ults. Champs that have not been mentioned that do well: Xin, Cass, Diana, Riven(immune to slows), and Anivia.

I had intense trouble with Jayce. Remember that lategame, Kayle beats everyone. Jayce can clear waves really well without being near the minions if he has too, and early game he is much stronger.