Should I go to a school I can’t pay off my first year?

BU is not possible. You cannot go.
Wpi doesn’t meet need so it may not be possible either.
If it IS affordable (direct costs = 10k) then it’s an excellent university, better than BU for your chosen field.
If WPI doesn’t end up being 10k, you have three choices:

  • a public university you can commute to
  • any university that offered you a full tuition+fees scholarship
  • the list of colleges that miscalculated yield (published in about a week).

What do you want to do with BME? Note that it’s the only engineering specialty that requires grad school -might you be able/willing to switch to civil engineering with an environmental concentration?