I lived with my boyfriend the whole year of 2016. I turned 18 in December of that year. I was wondering if he could claim me on his taxes and if I could also file myself?

You cannot be claimed as a dependent by him under the Qualifying Relative rules since your gross income for the year is $4,050 or more.

To be a Qualifying Relative -

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.

2. The person either (a) must be related to you or (b) must live with you all year as a member of your household. 

3. The person's gross income for the year must be less than $4,050 (social security does not count) in 2016

4. You must provide more than half of the person's total support for the year.

5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.

6. The person must not file a joint return with their spouse.