There is ways to bend the truth without lying.
I was fired from a job sometime back because i did say something stupid on my cv about the company that could have caused trouble for the company but i managed to wrangle round it by thinking up other reasons why i wanted to leave.
Sickness wise - i know my fiance had the same prob with some long term sickness time off which made job hunting harder but if you are just truthful - dont rattle on about everything bad happening at that time, just be straight to the point, you had recurring illness and family problems which you had to assist with - thats all you have to say and many accept this.
A lot of interviewers want to know the truth but if they see its a personal matter a lot skim over it.
Dont lie about sick days though - your previous employer informs them of any they have of you on record.
Just be confident and hopeful, make clear that you are fit and healthy and ready to show them what a great worker you are.
There are also some good help in a book i wrote up in this section - 5 steps to interview - i think its a sticky now but it does help if you prepare yourself for any other questions - you might seem quite shy about your attendance but make sure you have all the answers when you go in there and be fantastic
Im sure its just a little hurdle but if they are a good employer they will see something good infront of them

Sometimes a lot of shit happens all at the same time but just show everyone you are stronger and fit enough to carry on
good luck huni x