Are you married? Do you live with another adult? What is your estimated 2016 income?
You asked:
Can I file if I only worked the last three months of the year? And will I be eligible for head of household or child credit?
You must file regardless of how much of the year you worked. If you made less than the minimum amount for the year to have had to had taxes taken out of your pay, then you will get a return. Don't let that money go unclaimed by the federal government, it is your money after all.
You should claim your worked income as well as any unemployment / welfare / other income you made during the year.
Head of household is for the primary person who lives at the address. if you are only 1 person, then no, you have to file single, otherwise it depends on your status in the household.
Child tax credit is based on
A) your income level
B) If you have children that you can legally claim as dependents
C) If there are other circumstances that modify your eligibility for the tax credit.
Even if you are not required to file (due to low income) you would want to file to get back any withholding taken out.
Q. Can I file if I only worked the last three months of the year?