94 jetta oil light beeping

These Jettas have 2 oil pressure sensors: one for low engine speeds and one for high. The high-speed sensor starts acting at about 2,000 rpm, and if the oil is too thin for the wear in the engine it will cause the light and beep as you pass through that engine speed. After the 15-20 minutes the oil has heated enough to thin out, so that would explain why it starts then. At higher engine speeds it may develop enough pressure to activate the switch, so all may be fine on the highway. As the engine slows down, the pressure drops, maybe enough to cause the beep just above 2,000 rpm; which will then stop as the engine speed drops below that point.
Some brands of oil filters are also blamed for this - often Fram. Use an OEM German filter, like Mann.
What wt oil did you use - perhaps 10W30? Normal would be a 15W40, and on older engines many run 20W50 to avoid these issues.
It's always possible the pressure switch is bad, or the instrument cluster; but since it happened after you changed the oil, I'd suspect either the oil weight or filter.