NO, you can Not claim HOH. To have a Dependent, 1) they must not be MFJ, or 2) If MFJ, filing Only to get back tax withheld. Income of $34.6k clearly requires filing by itself. Income over $4,050 is normally too much for a dependent ...
IRS rules for filing status and claiming dependent exemptions: https://www.irs.gov/publications/p501/index.htmlhttps://www.irs.gov/publications/p501/index.html
