Hey again @Iamali97,
Thank you for getting back to me with more information about your situation.
Although I completely understand that it all seems very complicated, it's necessary that you have a closer look at my previous answer!
Unfortunately, there isn't much more that I can share with you: once you are at Frankfurt airport, please contact officials of the "Bundespolizei" (police) and let them know that you want to claim asylum and that you are 17 years old. Your passport will prove that you are a minor. They will then have to contact the Youth Welfare Office immediately and see if they have the necessary facilities to handle your case and take special care for you at the airport.
Of course, you should let them know that your mother is in Frankfurt, you can also let them know that she is outside, but I cannot tell you if that will make a difference and I doubt that they will let you go with her then - since you don't have a legal status to be in Germany yet. If you had a visa for Germany, you would be able to go with her. Without any legal status, you need to go through the asylum procedure first.
As I stated in my previous answer, you may be permitted to leave the facilities after just a few days, because the BAMF (Federal Office for Migration and Refugees) often cannot make a decision on asylum cases of minors within the set two days (airport procedure rules are special, therefore two days).
If your mother doesn't have a decision on her own asylum case yet, it is hard to say how that will impact your case. If she already had a legal status - residence permit - in Germany, you would also receive asylum as a minor, unmarried child of hers.
Please have another look at the previous answers I gave you and at the BAMF information I shared with you regarding airport asylum procedures and special care for minors.
One more thing: If you have any more questions, please try the comment function below instead of opening a new thread, to make it easier for others to follow the conversation :-)
All the best,