Thanks so much for the additional information.
It sounds like she may be suffering from laryngitis which is either going to be a primary condition or secondary to something else (the more common of the two).
Any irritation to the throat which might cause inflammation and/or swelling of the structures in the back of the throat could be responsible.
Infections such as Upper Respiratory Infections (aka Feline Flu), ingestion of irritating substances (such as grass), inhalation of irritating vapors, or post-nasal drip are possible causes and are responsible for most cases of laryngitis. Typically, the voice returns to normal within just a few weeks.
However, when the problem has been going on for a month, especially since she's older, then I'd worry that there may be something else going on such as a polyp or mass in her laryngeal area.
Since she is showing other symptoms as well such as lethargy and disinterest in food then a vet visit may be prudent.
I would dearly love to advise an over the counter medication for her but, unfortunately, there are none which will be helpful or safe in this situation.
I realize that my answer may not be what you want to hear but I would be doing a disservice to both you and your cat if I were less than truthful and honest in my response to you. I hope you understand.
I also hope that this is helpful and provides an explanation for what may be causing her symptoms. Deb.