Can apartment raise rent during my lease?

NO: the LL must give you notice of the increased rent. However, if you signed a new lease with the increased rent provision then you will be held to have agreed to the raise because you had actual and constructive notice of the new provision. If your lease is for greater than one year it must be in writing to comply with the statute of frauds. If it's not, and you didn't sign a lease, then your election to holdover and the LL's decision to continue to accept rent implies a renewed lease at the SAME terms of the previous lease UNLESS the LL gave you prior notice of any changes.