Although Bella was deaf, everything else about Bella was normal. At the very least, there were no defects in her growth, so Shelly could raise her up. It was just that every time she went to the hospital for Bella's consultation, the doctor would suggest that Bella had ear surgery as soon as possible so that she could recover better. However, Shelly did not have any money.
Even if she brought Bella with her to work and did not go to school, she still would not be able to earn that much money to treat Bella. Hence, she had no choice but to look for Mrs. Winter.
As such, she thought that it was better to put her stubbornness aside. It was much better to be living with the Winters than on her own. Living alone outside was hard enough, let alone with Bella.