I unfortunately use my larynx while I change my pitch, and I really don't know where or what or how to feel while I change my pitch without using my larynx. How do I even control my vocal cords without using my larynx? How are you doing that? I mean, how does it feel to you to change the pitch? Because if I knew it, I think I could stop using my larynx and start to control my vocal cords.
For me this required a good teacher to guide me to a fundamentally different mental model of singing. I don't disagree with Aaron's answer, but it leaves out a key element, which is breathing. People often talk about "breath support," and that has its own problems, sometimes leading to too much tension in the abdomen and too much breath pressure. The trick for me was to establish a gentle breathing action in the abdomen, without making any sound, but with definite engagement of the abdominal muscles, especially of the lower ones. Then he asked me to sing a single pitch in the middle of my range. The sound came with no sense of engagement in the throat or neck. The gentle breath pressure was balanced by gentle resistance from the larynx, but the resistance was imperceptible. I later came to understand that in singing a single pitch with my habitual technique, my larynx rose visibly, but when I sang this way, it did not. So, for me, the trick was to start focusing my mental model on breathing.
I say "for me" because I had a friend studying with the same teacher, and he told us not to talk to each other about what he was telling us to do. He said this because he was using completely different techniques with each of us, because we had completely different problems. Her problem was too much tension in her breathing, while my problem was not enough in mine.
If you can spend five or ten minutes in front of a mirror establishing good posture and breathing before singing a single pitch, and then, when you sing that pitch, observe that your larynx doesn't move, then perhaps you will achieve some success without a teacher. Otherwise, you would do well to find yourself a good one and take some lessons.
Your larynx is essential to changing pitch, so avoiding it is not the goal. It's the muscles of the larynx that control the vocal folds, which in turn produce your pitch. However,
none of the muscles inside the larynx can be felt or directly controlled (SOURCE)
A common problem for singers, however, is tightening the throat. One way to begin relaxing is to speak (not sing) slightly higher and lower than normal while allowing the top of your chest to feel heavy. As you change your speaking tone, you may feel sensations inside your throat, but the outer part of your throat/neck should remain feeling like when you're at rest and breathing normally (or close to it).
If you're singing quietly, you may find that singing louder makes it easier to hold a steady pitch. On the other hand, if you're pushing your voice to be too loud, that can put strain on it, and if you sing a bit quieter you may find the pitch control easier. Many artists will rely on Auto-Tune and other pitch-correction tools in the studio, but the technology has advanced enough where singers can use it in concert, too. You shouldn't feel tightness or pain in your throat. You shouldn't have to tense any part of your body to excess (abs, throat, shoulder, tongue, jaw etc). It should feel GOOD.
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