For tax purposes, if you provide over half of their support, you can claim your child and your girlfriend as your Dependents.
Since you and your girlfriend live together with your son, and you have the higher income, you can claim your child for the Child Tax Credit and EIC Credit and file as Head of Household.
Your girlfriend would be considered an 'Other Dependent' and would only be a $500 deduction for you, so you may not want to claim her if it would affect her other benefits.
Click this link for info on Who Can Be Claimed as a Dependent.
The rules for SNAP, WIC and Medicaid vary from state to state, but since you are not married, your girlfriend may be applying for herself and her son as a 'household', so that your income is not considered.
She could check with the agencies to verify this.
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