Can tonsillitis spread to other areas of throat?

Possibly: That depends in part on the causative agent, the treatment used, the immune status of the patient. The tonsils are in essence a part of the lymphatic system. Extension of infection as peritonsillar cellulitis, abscess, retropharyngeal abscess, cervical lymphadenitis, mastoiditis, sinusitis, and otitis media are all uncommon but real potential complications.

Yes: Multiple potential areas of spread, although these are relatively uncommon complications.