its a relative of chocolate, Kola, Okra and cotton. In itself the tree is gluten free. what some companies might do to it is another story.
Annatto that is making you sick might be for another reason.
I'd like to add a comment about my own experiences with annatto. I have been gluten-free for about 3 1/2 years now & have much less trouble than before. But I still react to things that I don't yet know what they are. Hives, swelling of fingers, palms, wrist, soles of my feet. But worst is when my tongue suddenly swells up, which happens a lot.
I have kept a food diary & have had suspicions about certain flavored syrups as well as eggnog & the margarine I use. I have finally narrowed it all down to the common ingredient of annatto.
The reaction is usually about 2 hours later. It is probably a true allergy & not an intolerance in the way the celiac thing is. I have found a margarine that has beta-carotene as a coloring agent & am going to try that out. Looking forward to a breakfast of gluten-free muffins, annatto-free margarine, & NO tongue-swelling.