Hi Xavier, welcome to the forum!
I totally understand what you mean by air hunger, that was my first POIS symptom ever, and for some reason, in my case it's linked to exercise intolerance. I'm no expert in this matter, but after having suffered from POIS for 13 years, I've come to the conclusion that at this point nobody has any clue yet about what causes it or what its biological mechanisms are, and so there is no treatment plan for it either. Different people have tried different things, experimenting by themselves, as there is still no doctor knows how to cure us. And even though there are some supplements and medications that have helped some people with their symptoms, I believe they're just targeting the symptoms and not curing the syndrome or addressing the cause. Some forum members claim they've been cured following different methods, but there is no universal explanation that I've seen as to why their methods work.
Personally, I've been taking niacin (vitamin B3) daily for a few months now, and it does help a bit since most of my symptoms are inflammatory (fever, swollen lymph nodes, fatigue, brain fog). But still, it hasn't solved anything for me, I still get symptoms and have crippling exercise intolerance. Some people take it before orgasm, and someone here said that taking niacin and matcha tea before orgasm prevented all the symptoms for them. If you browse the forum you'll see that many members have proposed explanations and treatment plans for POIS, but they don't seem to work for everyone, that's why I think they work to prevent symptoms and not cure the underlying cause of the syndrome. Still, it wouldn't hurt you to try some of these supplements (mostly vitamins and minerals, as they're mostly always good for the body, if it were me I'd stay away from taking any medication for a syndrome that isn't understood at all as you might end up worsening things, but you have to decide for yourself and talk to a doctor if you want to try any of the medications that have helped people here).
I believe that POIS has to do with some imbalance/damage/malfunctioning of the nervous system, or of some specific nerves. Your symptoms seem to line up with this theory, but I have no idea of what the link between urinary problems and air hunger might be, other than different nerves malfunctioning and sending the wrong signals (that's what many of my POIS symptoms feel like, but I have no idea if it's true or not, or what we could do to test this theory). To lessen the air hunger feeling, what I do is to practice diaphragmatic breathing for a few minutes, slowly inhaling through the nose and letting the air out through the mouth, focusing on expanding the belly and abdominal muscles as I inhale. My diaphragm and abdominal muscles seem to tense/seize up when I'm experiencing POIS symptoms, so expanding the abdomen as I breathe feels like pushing against a wall that doesn't want to give up. But as soon as those muscles relax, most of the air hunger and feelings of sickness improve quite a lot. Sometimes it helps to lay down on a flat surface to do this.
I share your urinary problems, too. Here's an example that happens to me every day: I always take a bath before going to bed. Well, I urinate before taking the bath, but as soon as I'm out (even if it's just 5 minutes later), I need to urinate again, and for some reason there's a significant amount of urine, as if the bladder hadn't been emptied properly. Then, when I go to bed, the position change (from standing up to laying down) makes me feel like I have to urinate again (most of the time it's true that my bladder is not empty again, but if I'm having POIS symptoms, sometimes it's just a phantom feeling and there's actually no urine left). Also, sometimes I need to hold my breath to be able to start urinating, even though there's a significant amount of urine in my bladder. I think I do this most of the time now.
I've had multiple tests done at different doctors and the only alteration they've found in me is a very high level of C reactive protein (a marker of inflammation) when I'm in full POIS mode and running a fever, and low levels of vitamins D and B3. The lack of specific alterated results in medical tests makes things really difficult for people with POIS, as it makes it too easy for doctors to dismiss us as patients with psychological problems, which isn't the case at all. It's immensely frustrating. But please take my advice on this: POIS is a syndrome that can get much, much worse with certain triggers, sometimes things we wouldn't have imagined that could harm us. If you want to take the time to read my case (the link is in my post signature), you'll see an example. So be very careful, take care and don't risk your health too much over momentary pleasure, however necessary it seems at the time. I wish I had followed my own advice earlier, I probably wouldn't be as sick as I am now.
