Stuffing

I love sugary foods and drinks, however eating enough of them to feel stuffed always causes me to get the worst headaches. Does anyone have any advice?

Eat less of them. You don't need to eat just sugary things when you stuff yourself. There are other foods too.

Simply eat less of them.
Fill up with a lemon-flovered tea without sugar.
Or have a big meal (soup, salad, lasagna, bread) until you're full, so that you only need a small sweet desert to satisfy your taste and being full at the same time.

In addition to the above, make sure you're still hydrating with water. A lot of times a headache is due to being not sufficiently hydrated, and sweet/sugary drinks and sodas DO hydrate you--like, if there's nothing else to drink, it's better to drink a soda than drink nothing--but getting enough water goes a long way.