You don't have a BA just because you finish up the credits. You need to be certified to graduate.
At minimum, to fulfill the law school requirements, you need a piece of paper that confirms you've been certified (ie. a proof of GRADUATION, not degree completion).
Usually, departments only do certifications right before graduation. At my UG, this is only done in October, February and May. Getting a certification in September would be too late. The OP needs to figure out something new.