Probably not, as oral chlamydia is rare, and fingering doesn't transmit STDs, so your partner probably won't get it. You should be avoiding all sexual activity for 7 full days, which I hope they told you.
If you've done anything else, you might want to get retested in a few weeks, and any partners you've had should be tested. You should also avoid having sex with any partners you had prior to testing who have not been tested and treated, or you could be reinfected.