Margaret
You can apply for ESA from the day after your SSP ended, you will need your employer to provide you with an SSP1 certificate, if this has already passes then you can backdate the claim by up to three months.
You will need a Fit Note in order to make a claim for ESA, the first two cannot be for more than three months duration, after that it is at the discretion of your GP.
We don't deal with Tax Credits on the forum, but I would assume that you need to inform them immediately.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems