You don't have to take the wheel off, but you'll get a better look if you do. I'm pretty sure you have either a bad sensor, or some debris in the sensor, there is no way the pads are bad after only 4k miles. I replaced my pads in the front with pads from Advance Auto Parts about 10,000 miles ago, and I've had no problems since, and I just checked them this weekend, almost no wear, and for only $36.00 for the pads, I'm stoked. I got the Weaver Silver's from Advance. We even measured the rotor's, and they didn't need replacing.
Good Luck