Syracuse does not guarantee to meet the full need for all accepted students. Even with a lower family contribution, you are not likely to get full funding to attend this school. You certainly can apply and also apply for financial aid…and see…but have another plan if the money is not forthcoming.
I hope you have options on your application list that have costs that do NOT exceed your mom’s annual income.
And really, there are some schools where you would get very good need based aid.
You don’t mention your dad, but syracuse is a school that also uses the Profile, and the non- custodial parent is expected to complete that unless they are no longer alive.