I'm a bit concerned about my just turned three year old dd, her tantrums are really starting to step up a notch and she's started to hit/hurt herself.
I've noticed these are happening when things are different to what she's used to, new faces, busy places etc. For example yesterday her nursery held a parents session, where parents were welcome to stay and join in etc, dd hated this as they were obviously a lot of adults in a small room (she's always telling me she's scared of 'big peoples', she means strangers she's great with family, friends, nursery staff etc) she spent a lot of time hiding under the table just squealing, when I managed to coax her out she just started thrashing about and hitting herself over the head, I took her home at this point and she was absolutely fine once we got in the car.
Another example this morning I really needed to pop to the shop, dd really hates it at busy supermarkets we normally have screaming fits or she will just lay down rigid in an aisle so I can't pick her up or anything. To make life easier for us both I tend to do online shop but today I just needed a few bits so planned to sit dd in the trolley seat and whizz round. Anyway she got that upset she started headbutting the trolley and bust her nose 
Once again as soon as we were back in the car she was her usual happy self, she's very chatty and inquisitive, very loving etc. Is there anything I can do to help her? Apart from avoiding the supermarket at all costs! I hate seeing her so upset when she has these outbursts. Anyone else's toddler do similar?