How wonderful that you were willing to adopt an old dog! They so deserve the love and care but most people are not willing to take on that challenge. Kudos to you!!!
To be blunt, I'm disappointed with the shelter. Chi's are known to have heart defects in the breed, it is something a shelter should take the time to learn about before placing a dog. They could have easily contacted the Chi rescue and made sure to do this. I realize that many shelters are overwhelmed, but to me that does not excuse taking the time with the dogs they do have.
Unfortunately you are in a tough spot. You need to balance the dogs quality of life with your financial ability. First, a question about the vet you took the little one to, is that vet intimately familiar with the breed? If not you might call around and find a vet who is, be that a cardiologist specialist or a very knowledgable vet.
You might also try contacting your local Chi rescue and see if they can give you a referral to a veterinarian.
Chi Rescue
Many Chi's live long happy lives with a heart murmer, many Chi's don't. You'll need someone familiar with this condition to advise you. Be up front with these people, they love the breed and want what's best for every dog. Tell them your situation, you adopted the dog from XX shelter, you are committed to the dog, the dogs quality of life comes first, but you are limited on finances. Ask them to use their experience and knowledge to help guide you. Don't expect them to make the decisions for you, that will be up to you, but do expect them to have the knowledge you lack. And do not be afraid to ask questions, no matter how silly you may think it is, and even if it's your 52nd question. Hopefully they can point you in the best direction for you and your new family member!
As you don't know me from the stranger down the street, a bit about me... I come from a family that has had Chi's since my mother was a child. There have always been Chi mixes or Chi's in my immediate family. I had a little 4.5 lb girl myself from puppyhood until I had to let her go at almost 16 years old (that was 2 years ago next week). I'm not a breeder, I just love the litte guys and took the time to educate myself about these special little dogs. Here's a picture of my gramma's girl Trouble (she's one of my favorites and know's it, yes, even though she's earned that nick name 
). Troubie is now about 11 yrs old and she has a heart murmer and is still going strong.
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tabitha
Kayo, Kahla, and Dante'
