Why is my budgie underweight?

I have two budgies I've had for about month now. I took one to the vet today because she is gagging and has diarrhea. They said she is very underweight. I feed them parakeet seed they sell at the bird store and give them some millet spray every day but I don't leave it in the cage. The vet gave me a dietary supplement to put in the water and Harrison's high potency pellets. I gave them half seed/half pellet but they pick they seed out and leave the pellet. They aren't tame. What can I give them to fatten them up? What reasons would they be underweight? How can I get them to eat the pellet? The vet suggested that I wet the pellets and syringe feed it but I don't know how to get hold of her without her going wild. HELP PLEASE