I have known about the device you currently use, as my father uses the same thing, and unplugs his cordless phone to use it. you may want to contact the manufacturer of your current device, and ask your health care provider to sent information about the device they have for rent. I would start there and google the manufacturers.
I am surprised that a cell phone versions is made. Ii have a friend who is hearing impaired and needs a TTY (TeleTYpe) device to read the other person's response. They do make one or two devicethat that plug into the headphone jack, yet not recommend for cell phone use. The concern is that a cell phone is very much like a network in that you have dropped packets, or you receive them out of order.