Disclosure: I'm a doctor, I specialize in rehab medicine and have a special interest in running medicine.
The first was just a douche who didn't understand why someone would run intentionally. The second was a sports doctor that I saw on a recommendation that told me to "ease into it, that'll be $300 please", the most recent is a sports doctor that was recommended to me by a friend of a friend that's a pro runner. He gave me prescription strength advil and told me to stop running for two weeks and see how it was doing. Well I was fine when I wasn't running but as soon as I started again I got knee pain! I went back and he gave me an extension on the prescription. Thanks but no thanks.
You've had bad luck with doctors, not your fault by any means, but they honestly all sound shitty to me. I wouldn't let any of my partners get away with that kind of behavior of those 3 doctors.
I dont know if you have a good primary care doctor, but usually the good doctors always seem to refer to other good doctors, while bad doctors keep referring their patients to other bad docs. I don't know why this occurs, but seems to be a regular pattern I see. I've seen shitty academic doctors as well as shitty private practice doctors.
You're problem seems correctable at this time. The relative rest and advil prescribed to you are to decreased any inflammation in your knee (but it doesn't treat the underlying problem), and as the inflammation goes down, you need to see a PT to address the musculotendinous imbalances that are causing your knee to hurt at 5 mins of running. You need a PT that will watch you run, walk, jump, squat, etc, then give you an exercise program of strengthening and stretching for you do at home. You only need to see a PT once a week, and then you do your program at home daily, even twice or 3 times daily if you can, and then go back next week for advancement or changing your exercises. You don't need anyone doing any passive modalities to you (heat, ice, ultrasound, estim, massage, etc... you can do that on your couch). That's a waste of your time and money.
If you want to PM me your location, I can see who I know in your area. I'm connected nationally, but there are still large areas who I wouldn't know anyone, but maybe we'll get lucky here.
... the most recent is a sports doctor that was recommended to me by a friend of a friend that's a pro runner. He gave me prescription strength advil
I'm so, so tired of being told to take fricking ibuprofen all the damn time. Things I have been diagnosed with that I was told to take ibuprofen for as the only treatment/main treatment include: carpal tunnel syndrome; tendon impingement in my shoulder; very painful never-quite-fully-diagnosed nerve issue in arm/shoulder; lower back pain, including an episode of such severity that I was unable to sleep for two days because it was so painful to lay down; and my current issue of hallux limitus which is causing pain in both feet, ankles, knees, one hip, and my back due to being unable to walk correctly. And every damn one of them acted like they were gifting me with some special doctor secret, or doing me a real favor.
Chronic migraines got a recommendation of Excedrin instead of ibuprofen, just for a change of pace.
That's because ibuprofen, despite being an old old medicine and over-the-counter, is still one of the most effective pain and anti-inflammatory medications we've ever invented. All our new medications are just trying to match the effectiveness of good ol' ibuprofen. Because they are new, they require a prescription, but they are not really any better. The same goes for acetaminophen (tylenol).
Pro-tip: advil gives it's analgesic effects at any dosage, but for the anti-inflammatory effects of advil to kick in, you need to take at least 800mg three times a day with food (that's 4 pills each time). I basically tell my patients to ignore the instructions on the bottle. Of course, obligatory dont take this advice without consulting your own doctor first.
For all your conditions you listed above, a trial of ibuprofen is absolutely the correct first step to take in the treatment algorithm.