I sprained my wrist over a month ago, i have been using a wrist splint but it still hurts extremely bad. how long does it take to heal?

Depends on injury: Severely injured soft tissue surrounding a joint can sometimes take weeks, even months, to fully recover. Depending on your original injury, you may require full time splinting for up to a month. Your treatment plan should be outlined for you by your physician ; should include gradual reduction of time in your splint and increase in pain-free activity.

A simple splint: From over the counter may be useful still. However the term sprain has many meanings, and is used to mean "negative" xrays by many but there can be a fracture not seen, a ligament injury, tendonitis, joint pain, carticlage tears , tendon injury and a whole lot of things thrown into the non fracture "sprain " category so if you are not better...... Get seen soon.