The easiest way to get an appointment is to search the internet. I recommend http://www.jameda.de/aachen/aerzte/gruppe/ . This website does not only list all sorts of doctors in Aachen, but shows photos from the practice and ratings from other patients.  Alternatively you could search on http://www.gelbeseiten.de/arzt/aachen or http://www.dasoertliche.de/Themen/Allgemeinmediziner/Aachen.html .

You are free to choose any doctor or specialist you like or need. If you have a cold, the flu, fever or some other common disease or if you do not know what sort of doctor you need, go and make an appointment with a general practitioner, in other cases it is faster to go to a specialist straight away.

Allgemeinarzt / Allgemeinmediziner
Zahnarzt
Augenarzt
Hals-, Nasen-, Ohren-Arzt / HNO-Arzt
Frauenarzt
Urologe

general practitioner
dentist
eye-specialist
ENT-Specialist, ears, nose, throat
gynaecologist
urologist

Search for this keyword on jameda and choose a doctor with a good rating who is nearby. Call the number published on this website to make an appointment. Emphasize that you need an appointment very urgently (if you do). If one doctor is not able to give you an appointment in near future, you can try to call another doctor. Sometimes they will ask you to come to the practice early in the morning and wait until the doctor has time left over to take a look at you. Sometimes- quite often – you will have to wait for a very long time in the waiting room. Maybe you’ll want to take a book with you.