P.L.
This can be very normal. I would make sure she is getting enough rest and nap/sleep time. My kids usually overreacted more when they were tired. (Me too)
Time outs are great - and are showing her that she is resonsible for her behavior.
If it gets worse - or if your gut tells you it's a deeper issue - I would see a specialist. Mom's usually have great instincts - so you decide.
I would also give her words to use - "I'm sure you are mad" "this can be hard..."
or even - "let's slow down and do this together"
Some of her frustration may be that she actually thinks she is as capable as you are. And when she is unable to "put the crayons away" she is reminded she is "little".
Sometimes I would encourage my girls - by reminding them how funny they looked when I first gave them a spoon and fork (or even how they looked when they just started eating "real" food). I would remind them that now they can eat without spilling too much - and also almost always hit their mouth on the first try. Show her how she is already learning and developing.
Try to lighted her mood - and get to the root of her frustration - and talk her through it....
As for public places - don't worry about what other people think - focus on your daughter and do what you need to do. Pick her up and carry her away to a better place if you need to. Do the time-out somewhere semi-private. If you are looking at the other people and trying to deal with her - you'll lose everytime. Once I sat on the floor in a store - with my daughter on my lap - until she stopped screaming. No one told me to - I just did it. It was my first instinct.
If you are out and stuck for somewhere to go - bring her to the car - and put her in her car seat - and close the door and stay outside the window where she can see you. Of course explain she is having a time out - and you are not leaving her - be firm and as loving as possible.
My daughter and I can laugh now as I remember when she was 4 years old and trying to kick me as I carried her out of a friends house. She's 16 now and a terrific young woman.
Good luck.