Because an anecdotal answer to why this involuntary action can set off an eyelid twitch is that the act of sneezing is quite forceful on the body, jarring and jangling things up, and the tiny, minute muscles of the eyelid get caught up in the act. One mechanism is that sneezing involves so many muscles in a coordinated movement, that ancillary muscles may be incorporated by the body to 'stabilize' itself. In fact, it's not uncommon for a sneeze to result in a fasciculation elsewhere in the body, such as in the abdomen or trunk. In conclusion, any kind of muscle fasciculation, including that twitching eyelid, following a hard sneeze, is absolutely nothing to worry about.
The sneezing may cause the active movement of the bacterium in the eyes which you get from the daytime touch. That is the reason for the right eyes to get twitching. You may go to the hospital to have a look. During this time, you'd better have a good rest for the eyes.