I am afraid this is the question to which you are unlikely to ever discover the answer.
It is completely normal that you can smell some molecule that others cannot smell. When somebody smells an egg, several hundred compounds (of the thousands or more present in the egg) dock to receptors in their nose, and the combination of the information of these receptors, plus all other information available to the brain (including seeing an egg, being in a kitchen, etc.) leads to the recognition of an egg. And the set of receptors one has is pretty much unique to them. So, for everybody, there is a different subset of compounds their nose detects when they are around an egg.
It so happens, that in an egg-eating culture, pretty much all of these compounds have a positive association. I may smell A, B and C and think "oh, egg, tasty!" and my neighbour might smell A, B and D and think "oh, egg, tasty!". But apparently, you have a rare case where you smell A, B and Z, and for some reason, Z is very unpleasant.
In the current situation, it is highly unlikely that this comes from a microorganism. Such an explanation is both unnecessarily complex, and, as you already noted, it doesn't give the microorganism time to multiply. It is probably a chemical thing where either something that was bound up in other molecules gets released in certain preparations, or a chemical reaction happens during the preparation and a new compound gets created. (And if it was, against all odds, a microorganism, it is obviously not a safety-relevant one: people would have noticed if these egg preparations were causing food poisoning left and right, even if they couldn't smell it).
So, the situation is:
- there are myriads of chemical reactions happening when you prepare an egg
- one of them has a product which you can smell and is very unpleasant
- the ability to smell this is really rare (else it would be common knowledge that there is a subpopulation of people who hate eggs prepared this way).
Finding out which exact chemical docks onto your receptors would be a multi-year task for a team of scientists with access to highly specialized equipment, involving regular experimentations with you as the subject. And if somebody did do it, then... all you have is a molecule's name. If preparing the eggs in a certain way releases that molecule, it will continue to get released. It is unlikely that you can do anything about it, short of selectively breeding a new race of hens whose eggs don't contain that compound, something that would take decades, if possible at all.
So, the most realistic thing you can do is to accept that you just hate that smell. In the grand scheme of variations one's genes can encode, that one idiosyncrasy is pretty compatible with a happy life - just stay away from eggs prepared in ways you dislike :)