I think it's more of a beauty therapist thing than a hairdresser thing and yes it would be fine to get it done while pregnant, the tint doesn't touch your skin.

The other thing I was going to suggest was perhaps try a more expensive mascara. I'd throw in a recommendation for Clinique, their Long Pretty Lashes version, it gives you an enhanced natural look rather than making you look really made up. (If that's the kind of look you like that is!) My eyes tend to be a little sensitive too, not like yours by the sound of things, but I've never had trouble with this one.