Lily
Get in contact with the Housing/Council tax benefits people. They should be able to assess things primarily over the phone and then ask for any supporting docs they may need later. This may go a long way to helping you with the rent/council tax and let you tackle the arrears. We have found them to be very helpful.
The reason for the appointment could well be to make sure you are getting any and all benefits you can and just to discuss all the options openly.
It will be extremely unlikely that they are going to throw you out. If you cant pay the rent at present then you should be entitled to housing/council tax benefit and things will be paid that way.
Hope this helps. Good Luck.
On the way to a brighter future....
Kind Regards.
Lee