I'm guessing you tried the ignoring the tantrums thing, so she progressed to hitting/kicking so you couldn't ignore her?
I agree you should see the GP or ask the school for help. The school can assign you a family support worker, and if you get a good one, they're fab. Have completely turned around the lives of a family at our school.
In the meantime, I'd say this. We're all mammals, and our behaviour all follows these simple rules. If a particular behaviour brings something that is perceived by the one performing it as good, it will be repeated. If that behaviour SOMETIMES brings something good, it will be repeated even more often than if it always does so. If it NEVER brings something good (or brings something bad), it will be repeated less and less until it is no longer repeated at all.
Now the above is known from years and years of scientific research, across many mammal species including humans. The tricky thing in humans, is to work out what a child is getting from a specific behaviour. Is it attention? Release of stress (esp true for ASD children)? Their own way? Whatever they don't like stopping? Control? While you're waiting for help, try to figure that out. Then see if there's a way you could remove the 'good' consequence for your child when she performs that behaviour. Alongside that, can you reward the correct behaviour profusely? So the bad behaviour gets her nothing, the good behaviour gets her lovely things (time, praise, sticker chart for physical reward...). You have to match the two so her needs are met (why she's doing this), and so she learns to meet those needs in a positive way.