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If you are the one living with and caring for the child, you should also receive the Kindergeld.
I assume that you have a residence permit according to §28 AufenthG related to your German child? If yes, you are in general entitled to receive Kindergeld. Only if you are in a pending Asylum procedure you are not entitled or if you are holding a residence permit according to §25 Abs. 3 other conditions would apply.
May I ask you why you registered your child with the father's address? I am afraid that this could lead to difficulties in future. Also, you would have to apply for Kindergeld at the "Familienkasse/Agentur für Arbeit" in your district.
I also would recommend you to get an own bank account - it is not very difficult. In general, they will transfer the Kindergeld to your account. In very exceptional cases you might also be able to receive a cheque. However, the Familienkasse is not paying it in cash.
I hope this helps and please get back to us if any clarification is needed or you have any further questions!
All the best,