From my research, sunflower seed are actually on the list of things to avoid with this condition. Here are some others to avoid: chocolate, peanuts, almonds, cashews, walnuts, pecans, brazil nuts, sesame seeds, coconut, and gelatin. Seems like a lot of nuts are on the list as well as sunflower and sesame seeds.

Sunflower seeds are actually known to be a trigger for herpes flare ups so I would suggest staying away from them.

Hope this helps you,
Chris