Can chlamydia cause tonsilits or the symptoms of tonsilitis?

Yes: It's called pharyngitis, sometimes also caused by concomitant infection with gonorrhea.

Yes it is possible: You can get chlamydia in the throat from oral sex.

Very rare: Chlamydia does not readilly infect the oral cavity. It happens sometimes by oral sex, but much less common than genital or rectal infection. When it infects the throat, chlamydia has never been found to cause tonsillitis or other symptoms. If this happens, it is very rare. (This is unlike gonorrhea, which is more common in the throat and sometimes causes sore throat or tonsillitis.)