First off be grateful for the second chance at life you got, chances are had you not been at the hospital when you started having trouble breathing you'd be dead, a pulmonary embolism can kill you in a matter of minutes, it's legit scary because it can happen to anyone at ANY time.
Now as far as the girl goes, reality is if you love this girl, you don't need ANY parents approval, if she can't be with you without the approval of parents then she may not be in it just for you, in marriage each of you should be enough for each other, if you can't be with your partner because you can't conceive a child for example then you are not enough for each other and shouldn't be together, same goes for each other's parentals, with that said...see where she's at, and let your parents know they need to be a little more mature, when is all said and done, your parents will age and won't be there for you, eventually they will die and all you'll have is your wife to lean back on, hell same goes for your kids, you raise them and they too will move on while you age and the only person most likely by your side will be your spouse, this is the circle of life and unfortunately people have lost faith in a strong relationship and think is all gravy to be alone, you live alone, you'll die with not a single person holding your hand and that my friends is much scarier than death itself.