I'm sorry you're going through this
I really am. It's such an unsettling time.
Firstly and most importantly. Yes, you do need to be off.
This will honestly happen without prejudice, organisations realise what a stressful time it is, stress related sickness is very common for the staff involved.
Secondly, although it's terrifying thinking about starting over, that department is clearly at breaking point and getting worse.
Would it be worth you being the early bird and cherry picking another area now?
Start having a look what/where is available and bagsie the position before anyone else does.
In my repeated experience of guiding staff through this hideous process - the ones that did this were by far the happiest and settled a lot faster as it was still their choice, rather than being given the dregs of what everyone else didn't want.
If you feel strong enough, ask whoever is managing the change for a list of the vacancies, and look in to them.
Your wage is safe, remember that to stop yourself panicking, it's the actual job title.
Who needs titles anyway 
Use today to rest, drink tea, try some relaxation techniques, have a bath and try and stop that busyness in your head.