I have had a sore throat for a week now. i am wondering if the painting that i did last weekend, without proper ventilation, would cause a sore throat?

Though it seems: possible, it is not likely. Unless you somehow ingested the paint, inhaling paint fumes should not cause a sore throat. Sometimes you can get asthma or reactive airway disease from inhaling paint fumes. You likely have sore throat from a viral or bacterial infection. Take some ibuprofen and if things get worse, see a healthcare provider for proper examination and diagnosis.