Should I claim independent if I am a under 24 and a full time out of state college student who supports herself?

So with the info that's Provided so far would she be able to claim earned income credit

No.Single taxpayers with no kids have to be 25 years of age or older.

I thought that college student who is not being claimed as a dependent by anybody and makes less than $15,000 and in school  could qualify for eic?

No.  See post above.  You have to be 25 or under 65 if you don't have a child to get EIC.

Or would it make more sense to have her claim head of household as I (her mother)  am disabled and on social security with income of $4000 or less, however I am not filing head of household as if claimed her then she would not have been able to afford health insurance so I am not claiming her.

Well, she still wouldn't qualify for EIC, although it would lower her income tax.  I think she WOULD have been able to get affordable health insurance through the exchange but probably not now (maybe next year).

If you provided over half of your own support, then your mother is not eligible to claim you as a dependent and you will claim your personal exemption for yourself on your tax return. Please see the following rules for what qualifies a person as a dependent for more information:

 There are 5 test that will qualify a child as a dependent as follows:

• Relationship: Must be your child, adopted child, foster-child, brother or sister, or a descendant of one of these(grand or nephew).
• Residence: Must have the same residence for more than half the year.
• Age: Must be under age 19 or under 24 and a full-time student for at least 5 months. They can be any age if they are totally and permanently disabled.
• Support: Must not have provided more than half of their own support during the year.
• Joint Support: The child cannot file a joint return for the year.

There are 4 tests that will qualify a relative as a dependent as follows:

• They are not the “qualifying child” of another taxpayer or your “qualifying child”.
• Gross Income: Dependent earns less than $4,000 in 2015.
• Total Support: You provide more than half of the total support for the year.
• Member of Household or Relationship: The person must live with you all year as a member of your household or be one of the relatives that doesn’t have to live with you see IRS Publication 501for a list of qualifying relatives.

Note that the Support test you bolded doesn't require the parent to provide over 50% of support.

Thank you.  I reworded to indicate that the child must not provide over half of their own support.

Given the facts as you presented you don't seem to qualify as a dependent for your mother.  You will find that claiming yourself will probably not give you any financial benefit, however, given the facts you presented. None of the AOC will be refundable.