I've been wearing contacts since 1986. When I first got lenses, I had to try out many different kinds to find one that fit without discomfort. Recently, they discontinued that lens! I had to start anew - ugh! Anyway, the first one I tried is fine - AND EASIER TO PUT IN!
I would make an appointment with the doctor for another fitting. Perhaps there is a lens that is thicker, easier to manipulate and won't fold or turn inside out as easily. I wear monthly disposables - in and out daily.
Touch the lens as little as possible
Put pointer finger in case so lens sticks to the end of it
Use other hand to take lens off finger, turn it around and put it on the end of my pointer finger, ready to go
LOOK at the edges: is it inside out? Flip it if needed.
Pull down on lower lid with middle finger (of same hand with lens)
Put lens in and blink many times, ready to catch it - just in case it flips out.
Some people fuss with the upper lid - I can't do it that way.
Even after all this time, I do have days where it doesn't work the first time.