My mom and I bought one way tickets to Germany (from USA) bc I have to take 3 entry exams at different unis. Will we be allowed in Germany?

I will stay in Germany and apply for a residence permit once I get accepted into a university there, and my mom is coming to help me with visa, phone, bank, and apartment stuff. I read that sometimes they don’t let you in Germany if you don’t have proof of return or visa. I don’t have a visa yet or a ticket back.... show more I will stay in Germany and apply for a residence permit once I get accepted into a university there, and my mom is coming to help me with visa, phone, bank, and apartment stuff. I read that sometimes they don’t let you in Germany if you don’t have proof of return or visa. I don’t have a visa yet or a ticket back. (We are leaving next month) I do have invitation letters for the entry exam from the universities but I don’t get acceptance letters until end of August. What should I do or should I even be worried?
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