You shouldn't have to wait two weeks for anything, unless it's a firearm, or maybe a baby, though that math could be slightly off on the firearm thing. To avoid doing it for doc appointments, hit up ZocDoc.
Just now launching in SD, ZD essentially acts as an OpenTable for doctors, reducing average waits to see new MDs from two weeks down to that very same day, and giving you the ability to book appointments and check out doctors' schedules online, though be aware that their three hour "meeting with Doctor Bridges" is most likely just meeting an optometrist buddy to play 18 holes at The Bridges. To get that thing on your lip looked at, pop
that thing on your lip! in your address and insurance provider, then search a list of more than 50000 appointments with available professionals in your area who're trained not to flinch when they look at your lip. And if you ended up trading your computer for a really nice Laserdisc player, they've also got smartphone apps, and will even text you a reminder the day of your appointment.
And because you're going to want people prepared to see said thing on your lip, inform ZD what you're coming in for and they'll hook you up with appropriate specialists, so you have no excuse to be a baby about it, unless you're going to the OB/GYN.