Welcome to our Forum. I will try to help.  The events that you describe, your having gotten chlamydia and your wife's conjunctivitis and ankle pain may be unrelated.  You did precisely the right thing to  have both you and your wife be treated with azithromycin, this should and has apparently, resolved your chlamydia infection.  Good work!

For your information, geographic tongue is a normal finding and is not related to any STI, including chlamydia. 

Whether or not your wife has reactive arthritis (and conjunctivitis)  is unclear, as is the possibility that her illness is related to possible chlamydia.  There are many possible causes of recurring conjunctivitis which can and should be evaluated by your regular doctor.  Conjunctivitis may be due to infection (most often viral), to vasculitis, or to other causes originating within the eye. Reactive arthritis is very rare, is less common in women than men, and when it is present can be related not only to chlamydia infection but also to other infections (like campylobacter, a non-STI gastrointestinal infection)..  I hope she does not have reactive arthritis as this does not respond to further antibiotic therapy but, instead, should be managed by a rheumatologist with anti-inflammatory medications.

As a next step it may be worthwhile for your wife to be evaluated by an internist or rheumatologist to evaluate the cause of her conjunctivitis and ankle pain.  To allow the doctor to consider all possible causes, it would be best to make sure that he is aware that she may have recently had chlamydia.  Take care.  EWH

Chlamydia antigen tests are rarely used, particularly to test urine specimens because of problems with their accuracy.  There are occasional falsely positive test results with these tests.  Your negative PCR test a week later following treatment however is strong evidence that, whether or not you had chlamydia, you did not have it after taking the azithromycin,

If your wife had chlamydia conjunctivitis, the azithromycin would have cured it.  Transfer of STIs of any sort from an infected genital site (i.e. your penis or her genitals) to the eye on a person's fingers however is very, very unusual. 

My sense is that you are asking "could this be" questions which will not help you to find out what is going on.  As I said before, if your wife has continuing conjunctivitis, my suggestion would be for her to be seen by her regular doctor or, if appropriate, a rheumatologist.  eWH