If I was dismissed from a school and had to leave, am I responsible for the last several months of the lease?

Although you left school, you are still liable for the rent for the balance of the term of the lease.  The lease is a contract between landlord and tenant.  Your obligation to pay rent will end either at the end of the semester or if the place is re-rented before the end of the semester.  If the place is re-rented, your obligation to pay rent ends.  However, if the new tenant is paying less rent than you were paying, you would remain liable for the difference in rent for the balance of the term of your lease.  The landlord has to mitigate (minimize) damages and would have to have a valid reason for charging the new tenant less rent than you were paying.  Market conditions would be a valid reason. 

The landlord cannot allow the rental to remain vacant for the rest of the semester without making reasonable efforts to find another tenant.  If the landlord does not make reasonable efforts to find another tenant, the landlord has failed to mitigate damages and the landlord's damages will be reduced accordingly.  Reasonable efforts to find another tenant will depend on what other landlords in the area are doing to attract tenants; for example, posting a sign on the property advertising the vacancy, advertising the rental on campus or in some student publication, advertising in the newspaper or a rental guide or online. 

It sounds like the manager is offering you a way out by applying the rent you have paid toward breaking the lease.  It would be advisable to get that in writing.