I won’t and I’ll not are both short forms of I will not. Both are used in English.
Are there any situations where one is preferred over other?
I won't is the choice when an emphasised statement or retort is given:
"You must do two hours unpaid overtime tonight."
"I won't! / I will not!" (not "I'll not!"; won't here connotes strong will)
"There's no other way - you'll have to drive the truck through the minefield."
"I won't stand a chance!" (preferred) ("I'll not stand a chance!" sounds weaker)
"I won't inform the police that the man who ran on to the pitch and thumped the player was your brother." (won't stresses my - perhaps concessive - non-involvement; I'll not would be an unemphasised statement of intent)
I'll not is also short for I shall not, but the will / shall complexities seem to be very unresolved and argued over.
Normally, you will use I won't. Only when not is somehow strongly linked to a phrase would you perhaps sometimes leave it as such and simply use I'll rather than abbreviate not. But it is fairly rare. I believe you will find it more frequently in older English. Using I won't always is your safest bet.
Thank you for your interest in this question.
Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).
Would you like to answer one of these unanswered questions instead?