The best champions outside of lane to counter Shyvana include Caitlyn, Varus, and Lucian. These picks are all great at countering Shyvana with high win rates over 52%. Even if these Shyvana counter picks are not taken opposite your position, it's not a good idea to take her into these matchups. They will most often destroy Shyvana.
Yet, if the enemy team brings either Galio or Rumble, Shyvana mains should seriously consider picking her, as she easily wins against these champs with win rates over 55% against each ofthem.