I'm new here and I'm not a breeder or an expert ball python keeper.

I have a one year old banana morph who has a respiratory infection. I took her to an ER vet and they gave her two shots of ampicillin over the course of two days and then gave me oral bytril to give her for the next 3 days. This was an ER vet in Nebraska, so her knowledge seemed a bit limited. She showed me how to open the snake's mouth but did not show me exactly how to inject the medicine. I tried to give the oral med to her today with a friend helping hold her, but we had a hell of a time keeping her still and I only shot it in her mouth (on what little I found on the topic it turns out youre supposed to stick the tube of the syringe down the hole in their mouths?). It was a bit difficult for the snake to swallow and it made her mouth-breathe.

I feel so bad about it. I don't want to have to give her the meds again if I can't figure out how to do it properly but my resources are also limited as far as help goes. Can someone please tell me exactly how to do it and inform me to anything that seems wrong about the situation? I feel like a really naive parent who wasn't taught how to properly raise a kid.