Yep I think it depends on the nature of the problem.
My rule of thumb is that if it's urgent or you can't get there safely on your own then you call an ambulance, otherwise you take yourself in.
Only trick is sometimes I'm not the best judge of the urgency. So far only been one case when I was told I should have called an ambulance rather than getting there myself and even then I don't think it was clear cut. DS had febrile seizures, I called the hospital once they'd finished (didn't want to move from him to get the phone before hand) and they told me to bring him in myself but make sure someone else drove so I could keep an eye on him. When we got there the doctor checked him over and said he was fine but that I should have called an ambulance as soon as they started.

On the tracheal tug note, yep my DS also had this and I also didn't notice it. Just took him to the doctor cause his cough had been going on for a long time. She called the hospital straightaway to let them know we'd be coming in. We did get ourselves there though. Then stayed a week on oxygen, ventolin, and antibiotics. Not at all what I'd expected from that doctor's visit.