Hi there,
I've personally applied for and received three TNs (for three different companies) on a return trip from Mexico. In Southern California, we simply drive to the border and park our car, walk into Mexico, cross the street and walk back. You enter a special building and tell them you would like to apply for a
TN and you go from there. Total time spent in
Mexico was five minutes, max, and that was literally spent walking over the pedestrian bridge to get to the other side of the road. As long as you are in the USA legally (and it sounds like you are) you shouldn't be treated any differently than if you were to apply when entering from Canada. Many Canadians apply for a TN at a Mexican crossing if it is more convenient for them.
I did the above at the Tijuana/San Ysidro (San Diego) crossing. I believe that any non-commercial-only crossing will work. I don't know where the closest POE is to you, but that should be easy enough to find out by looking at a map or asking people in your area.
No appt is necessary - I don't think they even make them. You just show up with all the necessary information (letter, diploma, transcript, etc) and go from there. In the past, I've been done in as little as 45 mins and as long as four hours - it just depends on the traffic and officers that day. The TN can ONLY be applied for at the POE when you are entering the country, not a consulate or embassy.
As for trouble, I assume you mean on the Mexican side of the border. I've never had any issues but I am a fairly big guy. If I were you, I would bring a friend with me to be safe and be sure to let people know your plan. Also, keep a low profile, don't wear jewelry and perhaps wear a hat if you are blond. Just don't do anything to stand out and you should be fine. Oh, and go in the daytime.
Two random suggestions that come to mind......first - go to the bathroom before crossing into Mexico and don't drink much. If you have a long wait to get processed, the only bathroom is back in Mexico and those aren't fun. Second, there is often a long line of Mexican folks waiting to enter the USA. I simply walk to the front of the line and tell them you need to apply for a TN and have never had to wait.