Hi OP
Just trying to work out the timeline of events from your post.
The last line of your first post says you "wish you could go back to the beginning of May and not take the job." Was that May this year, and you had the accident the same month you joined?
You were then off for 5 weeks. Were you expecting an increase in your hours based on your contract terms? Was the increase dependent on completing a number of hours first, or successfully completing a probation period?
Assuming the accident was mid-May, 5 weeks later would be the end of June. You then said you needed to ask for time off approx 5 weeks ago, which was early July.
How long were you back at work before you requested time off to help your eldest with their own health issues? Again your employer could be using this as a reason not to increase your contracted hours.
No manager should make you feel sick or anxious. They clearly have handled this badly from your description, but I don't think they have been unreasonable in not increasing your contracted hours if you have been unable to work your existing hours.
If you did start the job in May, you have very few employment rights. Unless you can prove your manager knew you were on the stairs and instructed you to answer the call, there is no claim; your employer will just say it was your choice to answer the phone.
I would think that if you keep submitting sick notes, they will simply terminate your contract with the minimum amount of notice and hire someone else. I suggest finding another job ASAP.
I hope it works out for you.