If you have sensitive eyes, you should pay more attention when wearing contact lenses. Firstly, you should wash hands with soap water, and dry hands with clean towl. Secondly, you should put one of them on your finger and place it into your eye gently. After that, you should blink eyes slowly to avoid dislodging contact lenses.
Place the contact lenses on your index finger carefully in case of damage to the lenses and make sure that the hollow side of the contact lenses is sitting up on your fingertip and the side walls do not stick to your skin. And then pull your upper eyelid upward with the index finger of the other hand and pull your lower eyelid downward with the middle finger of the one with the contact on it. Then move the contact lenses towards your eye calmly and steadily and place it on your eye gently, in the course of doing this, do not blink. After these, let go of your under-eye skin first in case of tiny air bubbles. As a saying goes that practice makes perfect, I believe after you put the contact lenses in your eyes for several times, you will be experienced.
I, myself, have very sensitive eyes too. When I just begin to wear contact lenses, it took me half an hour to put them into my eyes. Yet after a few months' practice, I can handle them within 5 minutes. Here is some tips for you. First of all, which is also the most important in using contact lenses, wash your hands thoroughly. Cleanliness can't be ignored at any step of wear your lenses. Secondly, wash your lenses with care solution. Use your finger tip to rub them in the solution carefully and softly. Be careful and don't use your nail. This step can kill the bacteria and help clear protein from the lenses. Then please remember to start wearing with the right eye all the time, which can help make sure you put the correct lens on your eye. If your eyes are dry, it might be more difficult to put them on. Apply some moisturizing eye drops, and then put the lenses on. Taking the eye drops in advance can help lubricant eyes, and pro-long comfortable wearing time. Before wearing the lenses, you also need to check whether it is on the right side. If the lens edge seems to flat out, it must be inside out. These are my experiences and tips. I hope they are useful to you.