I've had laryngitis that lasts over a week 4 separate times in the past six months with no other symptoms of a cold/sinus/or allergies. What coulditbe?

Vocal cord disease. If by 'laryngitis' you mean 'loss of voice or hoarseness' then you may have a vocal cord/larynx problem. The possible diagnoses are: vocal nodule, polyp, ge -reflux or tumor. You need to see an ENT (ear-nose-throat) doctor to get evaluated. The ENT can pass a small scope down to the vocal cords to get the correct diagnosis. If you are a smoker, this is a good time to quit. Hope you are better!
A few possibilities. The 3 main possibilities are: 1) post-nasal drip, even without other obvious nasal (rhinitis) symptoms; 2) laryngeal-pharyngeal reflux (lpr) due to acid refluxing up to the vocal cords; 3) vocal cord polyp. See md for maximal rhinitis and/or LPR therapy; if no response see ENT to check for a polyp.