Not if the OP is going back for an undergrad degree which it sounds like he would be since he only has one class in that major. At least most colleges are like that. I have an MS and if I wanted to go back(I do, for math, econ and art history) I would pay the undergrad tuition unless it is an actual graduate program but those are actually easier to fund since we can teach classes in exchange for tuition waivers + a stipend.

Depending on what state(assuming the OP is in the US) they may have credit limits on pell grants. My state caps it at 250 quarter credits. That doesn't affect actual tuition rates.

It is strange that they won't let you walk in the ceremony with your first degree if you have another degree pending. If you want to participate for your family, graduating and then declaring another major would be the best way to do that. You might want to talk to an adviser about everything.