How to deal with a toddler that hurts themselves out of frustration?

My toddler (2yo, 27 months to be exact) is in the throes of the terrible twos, tantrums and all. She's taken to hitting herself or hitting her head on nearby surfaces when she doesn't get her way (or just randomly unprovoked), then complaining that her head hurts.

The only thing I can think to reply is "we have to be gentle with ourselves" and offer her alternatives to relieve her frustration (counting to 10, hugging her bunny, hugging me, etc). But that only works like 20% of the time. If I try the tight squeeze hug to re-regulate her nervous system, she just squirms away. She's a big kid (37in, 32lbs) so it's hard to hold a squirming kid like that. It never works.

Am I doing this right? I hate seeing her hitting herself and bash her head on floors and tables. I feel clueless.