B737-700 First Officer reported loss of cabin pressure control. The flight crew requested priority handling and descended. The flight crew elected to continue to destination airport and make a precautionary landing.

Narrative

It was a normal flight up to the point that the Cabin Altitude Warning Light and Horn went off. It was less than five seconds before we had O2 masks on. We established comms and then Captain began coordinating for lower altitude while I started a controlled descent based on the fact that the cabin altitude and cabin rate weren't pegged. While working through the QRC/QRH the pressurization stabilized while descending and we elected to level off at 26;000 feet instead of 19;000 feet; which was our clearance.With the cabin pressure returning to around 6;000 feet; we elected to stay on O2 for a little while longer to allow for faster recovery from hypoxia symptoms. Checked the weather in ZZZ (VMC) and confirmed fuel requirements and elected to continue to ZZZ basted on the time en route; fuel requirements and weather at the field. I had symptoms of hypoxia almost immediately; which included tingly skin; chest tightness; heavy arms; light headedness; and a sinus headache. Most symptoms subsided within 20-30 minutes; but the headache lasted for several hours. We landed without further incident at ZZZ.