A red bump appeared on the corner of my lip. the next day, the whitehead appeared, when popped the pus came out. is this a cold sore or pimple?

Pimple most likely: From the description this sounds more like a pimple as it built up over time and came to a whitehead before it drained. Cold sores are usually more flat and shallow, moist looking and sting quite a bit. Either way, touch it up with a little Neosporin and avoid sharing kisses with anyone until it heals. See your MD to confirm the diagnosis.