I mean, it’s just eggs with some stuff in it, why would eggs have side effects. If you like having that for breakfast go for it. Nobody gets to decide what “okay” means for you, either think more about how eggs might affect your personal diet or whatever, or just let it go and enjoy your eggs
A 2-egg omelette is okay, but it honestly might not be enough. What do you add with it? Are you doing any type of strength training today? A better option might be the 2 eggs plus 2 egg whites. Add in vegetables, some cheese and a protein such as low sodium turkey or chicken deli meat.
I have started having two-egg omelettes from about 2-3 weeks ago and personally, I don't see any side effects at all. Despite what the media tells you, eggs are a very good source of protein, beneficial if you move around quite a bit. It will boost your intake especially if you don't have much of other proteins throughout the day!
Having a 2 egg omelette a day would probably make me super constipated and gassy. Lol so yeah I would have lots of side effects.