I might mention . . . that the rules of heraldry are a good deal more flexible in the Seven Kingdoms than they became by the late Middle Ages in the real world. There are no "laws" of heraldry per se, no college of heralds for enforcement, no formal regulations about cadency and differencing. So individual knights and lords have a certain amount of freedom to bear what shields they prefer and play around with their house sigils... or not, as the case may be. Thus Big and Little Walder, at Winterfell, quarter the arms of their mother's and grandmother's houses on their shields and surcoats, though they could just as lawfully wear the Frey towers unadorned. All three sons of Mace Tyrell are entitled to bear the Highgarden rose, and sometimes do... but when two or more of them are fighting together on the same field, you will often see Ser Garlan (the second son) with two roses on his shield, and Ser Loras (the thirdborn) with three. There is also the case of the harper/knight Pearse Caron in "The Hedge Knight," who chose to ride in the tourney with his personal emblem (a harp) on his shield, and the Caron nightingales on trappings and surcoat, and of course Raymun Fossoway in the same story, who births the green-apple Fossoways when he breaks with his cousin.
Robb Stark did something akin when he rode out of Winterfell in A GAME OF THRONES; you may recall that his shield bore a wolf's head, not the running wolf that appears on the Stark banners. Some of the old Kings in the North also had their own personal variants, undoubtedly, though I haven't yet decided what they were.
This sort of stuff happened all the time in the Dark Ages and early Middle Ages, where heraldry was unregulated and very much a matter of individual choice. It was only later that everything became formalized.