Hearing aids cannot hurt your hearing. They are programmed by audiologists to normalize your hearing, not to give you "super hearing" or anything that might approximate an over amplification of sounds.
I do agree that many hearing aids are ridiculously expensive. But reasonable ones also exist. Sam's Club and Costco, for example, offer affordable hearing aids. Hearing aid dispensers--rather than audiologists--also might offer less expensive models.
Here is an article about hearing aid expense from 2012:
Audicious is one of the better known companies that offer affordable hearing aids. I believe you need to give them a recent audiogram so they can program it.
There is scientific
evidence that hearing aids do help people with tinnitus. They do this by 1) stimulating your auditory cortex by providing sounds you are missing through hearing loss and 2) improving your ability to hear a variety of sounds, which may serve to distract you from your tinnitus.
Hearing aids won't cure your tinnitus, of course. And, I believe, the best hearing aids include some type of white noise component, which further helps to distract you from your tinnitus. That said, whether or not you want to wear a hearing aid is a personal choice, but it should not be choice made from fear that the device may cause hearing damage or may worsen your noise.