No, child support is to reimburse the parent with primary custody for the expenses that parent already paid for the child. It is NOT intended to help the non-custodial parent with expenses they voluntarily chose to incur. Sure, you could ask mom to help with the cell phone, but when she said no the first time (and you said that you asked her more than once) then you should have accepted that no.
Child support is to help cover housing, food, sundries and all of the other things that go into supporting a child. Again, in your case its you reimbursing mom.

