I just want to say that I think you are doing a great job. You are a new owner and you are here asking questions, getting help, trying out the things you are getting advice on. Most people would not be doing that much.
I also can understand that sometimes a vet bill given a family's financial situation is not always an option. However, you are willing to do this, if what you have done so far doesn't work. I think that is to be commended also.
Knowing what to do, for first aid at home, is vitally important regardless of the kind of animal that you have. I had horses for many many years and other animals and there were lots of times that I was able to successfully treat the animal. Because it was simple first aid. Then, of course, there were times that an emergency vet call needed to happen. Fortunately for me, there were times my wonderful vet was able and willing to walk me through what to do, and it didn't need him to come. (that was once when one horse colicked). (Horses like to have emergencies on Friday nights - rather than during working hours, at least it seemed like it) (3-4-5 in the morning - even better, more exciting)
I think it shows that you are responsible, mature young person. And intelligent too and very much love and care for your little budgie.