Delayed manuscript publication by publishers
Unless your paper was intended as part of a special issue, you absolutely should contact the journal to inquire about why the publication has not yet been published. In this digital age, three months is more than enough time to get a paper through the post-acceptance pipeline.

In your first email, I would just ask about the delay in publication. If you do not get a satisfactory response, then I would escalate and mention the need for the paper to be published to graduate.

Also, I would check with your school about the need for formal publication to occur. In many instances, an acceptance memo is sufficient.