For most people the injection might sting a little but not be painful. If she is going to do a deep cleaning you may be a little sore after but nothing a over the counter pain medicine can’t fix. No your teeth do not fall out because of bleeding gums. Your teeth can fall out because of the side effects from gingivitis if not treated. The needle they use to numb you is not freaky looking just a normal needle like what they use to take blood. Really it is a little smaller then that.
If you are still worried about the cleaning you are now going to get, go to your appoint a little early so you can speak to your dentist and tell her your concerns. She will be able to address any worries you have and make the visit go a smooth as possible.
I hope I have answered all of your questions.