They're is no such thing as sick 'leave'.
If you are reallynot feeling your best then of course you are entitled to take time off work for illness, but under these circumstances I would get yourself down the doctor straight away and explain why you are off work. Your doctor may sign you off for a couple of weeks if the strain of work is getting to you... assuming that's what you mean of course.
Your employer will not be happy that you resign and then call in sick, so make sure you cover your back as they could end up on the warpath with you.