DS is the same.
Honestly, forget the strangers, they would judge, then they would forget about you and move on with their lives. As hard as it is, why should you pay any attention to people who have no use in your life ? When I started thinking like this, I stopped caring what others thought when DS will get hysterical in public.
Your question "Is Autism going to get better ?". What do you mean ? if there's no strategies in place, then the behaviour will not get better.
I am quite strict with DS, I'm not sure if this is a good thing or a bad thing. When DS use to throw himself on the floor, I would pick him up and put him in his room...or if he has a huge meltdown in public. I would place him in a quite/secured spot and let him get it out of his system. It would It was very hard mind you.
Every time you are about to leave your house, go over some rules. Create a visual rule list/ showing what behaviour you expect from her and stick it on your front door. "Good Listening", "good talking" "But if you cry/throw a strop in the store, we would leave and go home (or we will have a break -- and go off to the toilets".
I'm not sure about your DD but with my DS, I realised that he felt these huge emotions but he couldn't express it. We worked a lot on emotions...not just identifying the basic feelings "happy, angry, sad" but emotions such as; "Anxious, worried, scared, bored, shocked, surprised". We would read simple stories and talk about the characters emotions. We also worked on "why" and because"...so eventually you are able to ask your daughter "why she feels this way and what is the reason". Black Sheep press have great visuals on working on "why and because".
You can do it ! It's a long/hard journey. But you and your DD will get there.