Will antibiotics alone clear up the cellulitis? If it doesn't, what's the next step? (Photo)

Infections are fairly rare after BBL if done by a qualified, board certified or board eligible plastic surgeon in an accredited facility- usually less than 1% risk. The cellulitis they saw on the CT scan may have actually been localized inflammation after undergoing the procedure. However, an in person examination and detailed history/review of systems would be needed. 
What you see may actually be what is called fat necrosis, which is when part of the transferred fat dies. The fat becomes hardened and may produce some surrounding inflammation. It is not due to an infection and may improve over time. 
Surgeons will usually want to see their patients to deal with any complications. Seeing the surgeon who operated on you will give you a better idea of the diagnosis and treatment options. If truly due to an infection, then it is possible there is a developing infected fluid collection called an abscess, which likely cannot be treated by antibiotics alone. This would require surgical drainage of the area. Following up with your plastic surgeon over time can help watch for this development through physical exams and/or ultrasound exams. 

It may represent fat necrosis. It can cause pain, lump,and even be somewhat red.  Sometimes they resorb,and sometimes they need surgical excision.  Best to be evaluated in person.