How about you try Trundle
? When they both hit level six, her ultimate helps your ultimate. Ulting after Shyvana ults will help Trundle steal even more resistance.
Olaf
is also good. I used him as a suggestion and as I read, he does out-sustain Shyvana in extended trades. However, it is always good to know how to play against a champion regardless of who you are using in the matchup. Here are some of the general tips that I found for countering Shyvana (note I use these tips and find them to be effective):
Avoid clustering when team fighting against a Shyvana, as Shyvana's abilities become AOE in her ultimate dragon form.
Play more aggressively when you see that Shyvana's fury bar is low. This means that she is not able to use her ultimate anytime soon.
Shyvana does not have any CC abilities, making her fairly easy to kite.
Champions that can slow Shyvana or speed up themselves and either kite or out damage her, while her Burnout is not active, are great picks against Shyvana. Examples of such champions are Kha'Zix, Aatrox, Kennen, Swain, Lulu, and Kayle.
Don't fight Shyvana while her mark is on you or she will deal massive extra magic damage equal to 2% or your max health per auto attack.
While Shyvana is auto attack reliant and is likely to build attack damage items, Shyvana's Burnout deals magic damage, which scales off bonus attack damage and the on-hit effect of Flame Breath deals magic damage based off the target's maximum health - this gives Shyvana high mixed damage that is difficult to itemize against.
Overall, it is better to build magic resistance over health and armor to counteract her kit's magic damage, though attack speed slowing items such as Frozen Heart and Randuin's Omen may help to lower her damage output considerably.