Such amazing art, I love it. Glad Equestria is safe and brought peace. We all know there is only way to save Equestria is give up the Elements of Harmony to the Tree of Harmony, which they had no choice. I am feeling Equestria will be fine.
A Prince/Princess can become one in other ways depending on the setting/situation (many Kings across history crowned themselves after conquering a country for example), it's not necessary to marry/be born into royalty (we also don't know for sure yet that Celestia/Luna were born rulers/Alicorns, unless it's in the new episode, so you're being a bit premature). In this case she both became an Alicorn (which we're still not entirely clear on what all that means) and she was declared a princess by the current royalty so... She's a princess for as long as she can retain control of her crown.