Why does my contact lens keep moving around the eye?

Hey guys!
It's my first time wearing contact lens, it's a soft type.
I know when the lens is inside out, I can recognize by the shape of it.
So the problem is when I put my lenses and close my eyes, they just stick to my inner lid and go upwards in the eye and I have to pull it out then, because it does not come down when I close my eyes again. Also, when I blink, my lens moves alot & vision gets blurry.
Should I get rewetting eye drops? Do they help?
Or What should I do?

Thanks! ;)

Added (1). Super Girl - Obviously! Majority people put it that way with index finger, looking up & like I said, I know when it's inside out - the sides flared out etc. I can recognize. You still did not answer my question.

Andrea - Nah, I don't think so.

Just like you said the shape, you can also tell if it is inside out if it isnt sticking to the pupil so you probably have been putting it in inside out. I would also recommend putting them in this way: with your index finger, hold your eyelid up and put the contact in your the index finger of the other hand.look up while you are doing up.once it is on your eye, move your eye ball around(left, right, up, down) until it falls into place.once my eye doctor showed me this, i have been doing it ever since! It might take a few tries but you will get it. And make sure you keep the contact moist!

Your dr may need to change your contacts. They could be too big or too small for your cornea. Call your dr and ask what they recocomend.