I have a bump on each inner part of my eyelids and they become irritated and swell everyother day, doctor said there a sinus, what else could it be?

Chalazion: It is most likely from a chalazion. They are similar to styes but are deeper in the eye lid. You can try to do warm compresses for 5 min at a time to see if they will go away. If they don't improve see your eye doctor. From the sounds of it, they don't have anything to do with your sinuses.

Punctum: Not sure what you're referring to when you say 'inner part of my eyelids', but perhaps you're referring to the nasal aspect of the eyelids where the punctum (puncti?) is located. This is where the tears flow out of your eye, into the canal then into your nasal sinuses. Occasionally you can get infections in this location and sometimes just irritation. I'd let an eyemd make that determination.