If your father or other relative does not live with you and  nobody can claim you then don't check the box that another taxpayer can claim you.

What would that do? What would happen then? Would I be claiming myself? Would no one claim me?

Yes.  That is how you claim yourself if another taxpayer cannot claim you.

Oh okay! Thank you so much for the help! Would the returns be about the same?

That depends on the amount of income.  When no one can claim you then you get all the credits instead of them.