Have you continued the medicines from last week or discontinued them as the ER doctor suggested? (All considered, I would continue them, but others here are more experienced.)
You might consider moving Buddy to a smaller cage and/or remove some of what is in the cage so that it is easier to catch him. I have had to do this many times with untamed birds (I foster for a rescue) and it helps make everything less stressful. It helps to even just remove things from the lower part of the cage. It also helps to darken the room if possible. (I sometimes cover a small cage and take it into a closet or interior bathroom and keep the light dim.) I use a lightweight piece of cotton fabric to catch them rather than a towel so that they don't catch their toes in the fabric.
Also, I think you were correct to decline a blood test and X-ray at the ER vet. The closest I've come to that situation was at my regular vet office on a weekend. The was only one vet and she was not an avian vet, though she had some experience with birds and other exotics. When she mentioned the possibility of doing a blood test, I (politely, really) asked her if she was sure she could draw the blood without killing my bird. She ended up not doing it.
Also, for an X-ray to be useful, I'm pretty sure they need to sedate the bird, which is also potentially dangerous. None of the avian vets I have used draw blood on a budgie without a very good reason; they have never suggested it with any of my budgies, even when they were ill. Cockatiels are enough larger that it's a different matter.