to answer your first question: the answer is yes. all relationships require an active sex life to remain functional, healthy, and 'new'. this has always been the case with relationships.
as for you wanting a relationship without sex, there is nothing wrong with that. everyone looks for something different in a relationship. your desire is not unrealistic. sex is not entirely essential for a happy relationship, but it certainly keeps the relationship "alive and going". you just need to find a girl that shares the same view as you. that is, if you really do feel this way. maybe the reason you seek a sexless relationship is because you're afraid of having sex? think about it.
lastly, i would like to give you some advice with your women trouble. many guys are shy and afraid to approach a girl they fancy - it's entirely normal. even those guys who seem very confident tremble in their socks when they're approaching a girl they have strong feelings for. it's harder when we place the girl in such a high regard (i.e., she's very beautiful, talented, smart, popular, too good for me, etc). keep in mind that she is just a person, not a goddess or other supreme being. you need to start taking the steps of getting out of your shell now (while you're 19, still in college where there tons of girls) and make it easier on yourself in the future. what are you most of afraid of? being rejected, right? who doesn't get rejected? what's the worse that can happen? she'll say no...so? try again with a different girl. imagine yourself asking her on a date and her saying yes, how amazing would that be? it's possible..but only you can make that happen. trust me, asking a girl out gets easier. it's really not that hard. girls aren't too hard to please. they are just like us, except softer and they smell nicer. :) i really think you should ask this girl out on a date. good luck. i hope my answer has helped you even a little.