These drugs were originally diabetes drugs, that had the side effects of weight loss, but that wasn't their original use that they got FDA approval for.
So they are going back and getting them approved for different uses, and maybe one of those will get by the insurance company. I saw one being advertised for Sleep Apnia, which is common in obese people. It works because when you lose weight, your Apnia usually improves, so while they aren't selling it specifically for weight loss, that's the mechanism that improves the Apnia. Maybe your doctor can get it approved for that reason, or another one.
I was 350, and I've lost 100 pounds, without the drugs. I quit all sugary beverages, and only drink ice water or unsweet tea. I only eat when I'm hungry, and only until I'm not hungry. It allows me to eat whatever I want, but in strict moderation. It doesn't feel like a diet, though, because when I'm hungry I eat, but only until I'm not. I never eat more than a half sandwich. I will eat cookies, but only two, not half a package. When I have craving for chocolate, I'll eat 4 or 5 chocolate chips, one at a time, and let them melt on my tongue, so my chocolate craving gets fulfilled, without an entire candy bar.
And importantly, I developed a distraction. My Dad quit smoking years ago, by doing a Rubik's Cube whenever he got a craving. I took up the guitar. I keep an acoustic guitar next to my chair, and if I get a craving, instead of heading to the fridge, I pick up my guitar.
I didn't even increase my exercise, although I have a pretty physically active job. I've plateaued now, so I think it's time to increase my exercise for the last 50 I'd like to lose.
Keep at it, don't give up. It is far easier to lose weight at your age than after about 30, so do it now. Keep making adjustments in your diet and exercise, and eventually your metabolism will shift and start working with you.