[Blindtlk] Two questions about administering medicine.

[Hyde, David W. (ESC)]

For the first, forget the spoon. Go to a pharmacist and get one of those graduated medicine measuring devices that come with most cough syrups. That way, you can measure the correct dosage and let her drink it from that.
The second is harder. The first thing to do, is for you to get comfortable giving injections. Talk to a medical professional and get some syringes and needles with which to practice. I understand that nurses start by injecting water (well they say it's water) into an orange. As far as feeling the point of injection, wipe the site first with a sterilizing agent. Some health professionals use thin latex gloves, and I've seen a few who use plastic ones, similar to sandwich bags. This would keep your hand from touching the disinfected site, but retain most of the tactility. 
Finally, please remember that your fear is contributing to that of the child. It will be easier to manage hers after you master yours. Be proud of what you're doing, and of that mom. There are very few of us, other than those with diabetes, who have to give injections. The fact that the mother believes you can do it says much for you. You might get more ideas from our Diabetes Action Network.
Good luck, and keep trying. Oh yes, oranges almost never cry when injected.