well done on phoning the paramedics!!!! You can NEVER be too careful when it comes to a little baby.
Remember to keep checking on her and look for any blueness of her lips. This will be the first indication that she isn't getting enough oxygen in her system. Oxygen is the essence of life and with continued low levels this can sometimes cause hypoxia which is lack of oxygen to the brain.
This will be a scary time for you two. But since you have a really good eye for when she is not doing to well, I'm sure things will go ok.
I'm sure she won't be "lazy", she's very sick and so will be tired. I went to hospital with pneumonia a few years back and it knocked me completely! I was in hospital for 4-5 days and that's with an adult immune system. A 3 month old baby has 35% of an adults immune system and that's if you're breastfeeding. It will be less if bottle feeding. Her little immune system will be in overdrive which will make her even more tired.
Don't feel bad about giving her all of the medicine. She will be a LOT worse if you don't give it to her. They all play their part in making her get better...
Best wishes for a speedy recovery, you are in my thoughts.