How about having a chat with your HOD to find out his/her plans for you instead?
Frankly, I feel that it may not be easy for you to switch jobs now and it may end up becoming a potential stressor for you if you are unable to find a suitable one. Hence, you can explore what the lateral transfer would be for you. Perhaps there will be a position with more regular hours which would be good for you as well.
Take care mummy. I hope things would work out well for you!
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