I've read that it can take several visits for a new contact lens wearer to learn to insert and remove them. If you've paid for the fitting, they should take the time you need until you can learn to put them in and remove them yourself. If not, ask some of your lens wearing friends if they had trouble learning, and who they went to. Maybe your parents would let you switch doctors to someone who can teach you better.
A trick I've read about for getting lenses in: Hold your eyelashes and eyelids open, using one hand for upper lid, other hand for lower lid. (Maybe you could practice this part at home, with clean hands, before going for your next try at a fitting.) Look up, and put the lens (soft lens) on the lower white of your eye. Gently release lids and close eye. With eyes still closed, look down, to get the lens to center on the eye, then open the eye. Since you're not looking at the lens when you put it in, you're less likely to blink (doing it more by feel).
A trick for getting eye drops in: pull your lower eyelid down, making a kind of cup. Put the drop in that "cup" of the lower lid, then gently let the lid go and close the eye. I've had to use eyedrops several times daily since January and my Mom taught me this trick (she's a nurse). I use it all the time and it works very well for me! I hope it helps you.