My cat is still very sick despite many vet visits

[Birdiebonita]

Hi there. My girlfriend's cat, Birdie, was a stray. In 4 months I've never seen Birdie healthy. My girlfriend says she's always been sick.

Girlfriend had taken Birdie to the vet numerous times. I know they've tried a couple different antibiotics and childrend's benadryl, but nothing has improved her symptoms.

Birdie is visibly worn down. Her tail was busted as a stray, she's very small, definitely was the runt of the litter. Her fur is always a mess if you pet it.

She has cold-like symptoms:
1.) She has a wet cough. She'll get real low to the ground and start heaving like a hairball but you'll hear the sound of phlegm deep in her lungs. She will strain and cough about 15 times she loosens the phlegm in her lungs. When that happens she will cough a big glob up and choke on it briefly and then swallows it.

2.) Sneezing. She might honestly sneeze 100 times a day. Often times she sneezes in bunches. It's just a rapid fire of 10 to 20 quick sneezes. Snot gets everywhere. Each sneeze produces thick snot that covers her face and nose. The floor/wall/blanket/or person in the fire zone also receives thick blasts on cat snot left from the explosion.

3.) Very congested breathing. She's very loud. When she eats she has to stop and breathe out her mouth just to get air. You can hear her constantly.

Vets haven't been able to figure out anything to alleviate the symptoms. I feel bad for the cat. It's really kind despite being sick all the time.

Anyone have any ideas to help her?

When I get home I'll post some videos of the events if that helps.