A General Aviation pilot reported turning onto crossing Runway 11 instead of Taxiway H after landing on Runway 34 at HPN.

Narrative

I was finally allowed to land at HPN after being asked to hold over the bridge; do 360s multiple times and rejoin the downwind; and being asked to go around once on final to accommodate the numerous jets that were also landing at the same time. It was extremely bumpy at pattern altitude. All of this information is relevant because I was quite frazzled by the time I landed. I had checked the taxiway diagram; but that was before all the 360s. I couldn't review the taxiway diagram carefully again because I was too busy trying to stay right side up while doing 360s in turbulence. I had planned to make Taxiway K after landing on Runway 34; but because of the gusty conditions; I carried a bit of extra speed and couldn't make the turn to K. After I landed; Tower asked me to turn left on Taxiway H. I didn't realize that H was a sharp turn to the left and intersected Runway 34 at the same point as Runway 11; and turned left on Runway 11; which at the time was not handling any traffic because of the direction of winds. The Tower Controller pointed out that I was on Runway 11; said it wasn't a problem; and then gave me further taxi instructions to the FBO. The gusty conditions; the stress of being repeatedly asked to break off my downwind leg and do 360s in those bumpy conditions; and the nature of the intersection; all worked together to make me miss the assigned taxiway and turn on to the runway instead. In the future I will take extra note of any multiple runway and taxiway intersections even if they are not designated as a hotspot and mentally prepare for a possible turnoff there even if that is not the one I anticipate using.