Unless there are special rules for sole traders (and this is an area I know nothing about), you would have until 31 Jan 2017 to file (and pay) the self assessment.
The tax year is the same for sole traders.
As for the payments, they split them up so you pay half in July and half in January. For example, on the 31st of January 2016 I paid the second half of my 2014/2015 taxes, and the first half of my 2015/2016 taxes. The second half of my 2015/2016 taxes is due on the 31st of July 2016.
"How do they know how much your 2015/2016 tax bill is if the tax year hasn't ended yet?" you may be asking. They guess, based on your previous year's tax return, and the payments are adjusted if the amount of tax to be paid is more or less than the estimate.
For me, this becomes exceptionally complicated if I try to think about it using my non-accountant mind. Happily, filling out the self-assessment online isn't that hard.
EDITED TO ADD: I typed some of this while the OAP was editing their reply, which is why some of the info repeats what they said.