Your not blind and you do notice red flags because you've pointed some out, like the constant attention to her phone.

Your problem is more that you willingly accept poor treatment because you think it is better than nothing. Start raising the bar on what you expect. If I go out to lunch with another female and she keeps looking at her phone, I'll be slow to do lunch with her again. And this is not someone that I'm dating and considering spending my life with.

Your girlfriend may just have some bad habits. Help her to break them. Woukd she put up with you making her feel ignored? I doubt it.