She's the woman in a hetero relationship, and their passion causes her to go through a lot of discomfort and sacrifice. It's not like they were trying for a kid... And in Elayne's case she gets no active or regular support in her pregnancy from her man (because of circumstances). So her annoyance makes a lot of sense, whether it's just half-hearted or a bit more earnest. And in Randland, you lose the ability to channel normally...
Although opinions vary, I didn't find Elayne to be a b!@#$ - she gets to hang out with Egwene and Nynaeve all the time for comparison. And I'd say that Elayne has great reason to be self-important: she's the main heir to a throne and her nation is riding on her. She not only has to think about herself because a lot of people are riding on her, she has pressure to live up to her ancestors' accomplishments.
Rand turned to her for help with the nobles in Tear, and I always thought that was the basis for their initial chemistry turning into something more serious.
I agree with you about Min, though - she really outstrips the other women for building a relationship with him. Then again, she has the least responsibility of them all...