'over one's head' is correct and can be used in written English.
It is usually used to describe something that is too difficult to understand or comprehend. Example: The Statistics professor's lecture was over my head and I couldn't keep up with her.
After the operation it will be hard to manage pulling clothes over one's head.
After the operation it will be hard to manage clothes that need pulling over one's head.
Funds for housing are difficult to obtain although having a decent roof over one's head is one of the basic needs in addressing poverty particularly in rural communities.
Still, it had seemed different with a sturdy roof over one's head and all America's rescue systems in the background.
With more money going on keeping a roof over one's head and necessities like food, there is less money to spare for things like holiday shopping.
There are so many charities to donate to and so many diseases to eradicate, and dumping buckets of ice over one's head to post the film on Facebook seemed too silly – too much of a celebrity-driven trend – to have substance.
A neon light went on over one mom's head when she thought of a brilliant way to teach her kids chemistry -- a periodic table version of the game Battleship.
Although they didn't rape her or her sisters, once they broke a dish over one sister's head, and they beat her brother.
Ordinarily, I interrupt -- turning tables at a steady clip is part of my job -- but up close I could see their tears and hear pieces of the story, about things flying over one woman's head and the final time she'd seen someone, and I kept slipping away.
Even poking one's head over a fence to comment on conditions about which one is concerned is an invasion of privacy, as evidenced in the adage "good fences make good neighbors".
To read Peter Paterson's life of the former foreign secretary Lord George Brown, for example – a man who could have become prime minister in the 1960s – is to shake one's head over its subject's ability to prosper in government despite his habit of becoming "tired and emotional" at the drop of a hat.
