It is very hard to help troubleshoot without seeing a video of your kicks. You could have a range of problems, and so, without playing 20 questions with you, I'll give you a list of things that are common to people who have kicking problems as you describe. It's probably better for the community anyway. Understand that what you describe often happens to new students, so likely, it is just your body getting used to all of the motions required to execute the technique.
Many of these tips can help correct many different kinds of problems with many kinds of kicks.
Lift the knee
What we strive for is lifting the knee, but danger can set in. Ideally, we want the knee as far into the shoulder pocket as possible, and then the foot whips up. This is dangerous because the technique relies on the momentum of the foot to whip it upwards. If you are not flexible, you can easily pull or tear a muscle. So start light and get an idea of your capability, then work so the knee goes ever higher.
When I ask a student to throw a kick, I sometimes ask them to hold the kick as long as they can. When they throw the kick as high as they can, but the foot immediately drops a few inches, it means they're more flexible than they are strong. Momentum got the foot up there, but with lack of strength, they can't hold it there. If this is your case, working on abductors and lower back is key. You can keep practicing the kick full speed, or you can do it using dynamic tension, or you can have a partner help you apply resistance (isometric / PNF). These exercises will not only build flexibility, but they will also build strength. And strength is important because it helps you control your kicks. Without control, you are more liable to injure yourself (because of a pulled muscle) or a partner.
Where are your hands?
If you drop your hands to the side as you try to kick, that can sap a lot of momentum from lifting the knee, and that can tend to keep the knee down.
What are you looking at?
If you keep your chin down during the kick, that can help create the tendency to keep the knee down as well. You want your chin forward - not upward and not downward.
Where are your shoulders?
If you hunch your shoulders, than can also create the tendency to keep the knee down.
Pivot on the standing foot
It isn't always necessary to pivot on the standing foot (indeed, there are times you don't want to). But by pivoting, even just a little, you can open the hips just a little more. This can help allow the kicking knee to rise a little higher. Buy not pivoting, a tight hip can tend to keep the knee from rising as high as it could.