As I said it comes from the lungs and the whole respiratory system in between. Mucus that comes out your nose doesn't just come from your sinuses, it comes from all the little hairy mucus producing tubes leading to your lungs as well. Anti-histamines do not primarily stop snot production, they counteract the effect of histamines, which have a side effect of making your nose run, but have other effects too.
*Boring science post warning*
The mucus from your sinuses is produced in your sinuses.
Whilst the lungs and other parts of the respiratory system DO have mucus producing glandular cells, the digestive and respiratory systems merge in the throat and oral cavity, which is primarily lined with non-mucus producing stratified squamous epithelium.
The glandular cells of the respiratory tract do have cilia ("hair"), and normally the mucus sits on top of this hair, trapping stuff (dust, pollen, bacteria, etc). The cilia move the mucus towards the nearest exit (in the case of the lungs, to the esophagus and for the sinuses, the back of the throat or the nose).
I suppose there is a teensy chance that some of the mucus produced in the lungs *could* move up through to the sinuses, it's pretty unlikely as it would have to pass through the throat (squamous lined section that is smooth and non-ciliated.) The body likes efficiency and that's just a waste of energy.
Sorry. Couldn't resist.