It takes some getting used to. Some people can just never get used to it, or never feel comfortable with contacts in their eyes.
Most of the stories about people who first get contacts involve how long it took the first month or so to put them in and take them out. Eventually, with time and much patience, many people get used to it, and sometimes even used to the feel of something foreign in their eyes. Others cannot, either because it remains just too uncomfortable to keep in their eye, or can’t get over the squickiness. (nothing wrong with that, either, I could never be a doctor/nurse, because at the mere mention of a needle or blood I feel faint - everyone has their squick level!)
Myself, I’ve been wearing them since I was fifteen. Took a while to get used to, and I, too, used to twitch, blink, and generally flip out whenever anything came near my eyes. Now I can pop them in and out at will, without a mirror. I’ve removed, cleaned, and inserted them both as a passenger in cars several times - though I would not recommend this to everyone! I remember mentioning to my father once, when I was about seventeen, how weird I thought it was that I had no trouble with my contacts, when only a couple years earlier, I couldn’t touch my eye with my finger (as I had seen some boys do in school, trying to gross the girls out). My father said, “The eye is stronger than most of us think it is, it’s not jelly-like.” For some reason, this comment took a lot of the ick-factor away for me. Contacts, eye drops, heck, even eye-liner was suddenly easier to use.
The only one who will know if you can get used to them is you. Do you have the patience to get used to them, and the technique to put them in? Do you have the will to get over the ickiness? Past that, are they comfortable? Are they unbearably uncomfortable? Sometimes discomfort isn’t just a “get used to it” issue, sometimes they are and always will be uncomfortable. It all depends on the type of contacts you are wearing, and/or what type you are able to wear, and how sensitive your eyes are (they will naturally be sensitive at first, they’re not used to having anything in them). Most contacts today, I find, are very comfortable, as they are soft, flexible, and breathable. But for some, they’re just not.