Yes. It is possible to get discomfort to remove contact lenses, especially when you suffered from dry eyes. It even hurt the eyes if you remove the lenses roughly. To help the eyes, you can apply eye drops first to keep your eyes moist, then you can remove the lenses gently. You may feel vision blurry or something discomfort in your eyes after you remove the lenses. It is OK. Your eyes just need sometime to adapt the processes.
Of course this is not normal. Once u feel uncomfortable, it means that something wrong is happening. I guess there are two possibilities. U may get an eye irritation cuz of your contacts. And the other reason is that your eyes may be sensitive to contacts so that you can not wear contacts. No matter what is the real reason, I think you had better stop wearing contacts for a few days cuz which will only worsen the situation.
Firstly, you need to make sure that you have washed your hands before moving your contact lenses. Secondly, make sure that you follow the right steps to moving your contacts. To remove soft contact lenses, look upward or sideways while you pull down on your lower eyelid. With a finger, gently maneuver the lens onto the white of your eye. There, you can very gently pinch the lens together with your index finger and thumb and lift it off the eye.