Thank you for reaching out to us and Welcome to Wefugees.
First of all, here is some information on how to apply for asylum in Germany:
And this PDF (in German) by BAMF can be very helpful with understanding the overall procedure: https://www.bezreg-koeln.nrw.de/brk_internet/leistungen/abteilung02/20/info_asylverfahren.pdf
As you can read here, you can apply for asylum at any state agency in Germany, for example the police, a reception center, an immigration authority or directly at an arrival center. You will have to make clear you want to claim asylum and register with a reception facility (Aufnahmezentrum). The Federal Office for Migration and Refugees - BAMF - will be responsible for your case.
Unfortunately, asylum applicants don't get to choose where they will be allocated or live. That is due to the "EASY" quota system and the "Königstein Key". Basically, it's a system that annually calculates how many asylum applicants will be "distributed" to each Bundesland, to ensure a "fair distribution among the Federal Länder".
Find more information by the BAMF here: http://www.bamf.de/EN/Fluechtlingsschutz/AblaufAsylv/Erstverteilung/erstverteilung-node.html
Here is another helpful article by Refugee Council Niedersachsen on How to Apply for Asylum (in German, please use a translating tool): https://www.nds-fluerat.org/leitfaden/1-der-beginn-des-asylverfahrens/12-wie-und-wo-stellt-man-einen-asylantrag/
If you consider applying for asylum, you can first go to a refugee support center/ refugee council and talk to them about your situation. They have experts there who can help and give advise on your options.
You can find a list of support services for refugees in Cologne on page 54: https://koelner-fluechtlingsrat.de/userfiles/Netzheft2018.pdf
I hope this helps. Feel free to reach out to the community again if you need further support!
All the best,