If your wife definitely has a genital chlamydial infection, then she caught it sexually. You don't say how long you two have been together, but if it is under a few months, either of you might have brought it into the relationship. You should also be tested, even if you have no symptoms and haven't had other partners recently.
Yes, chlamydia can cause
conjunctivitisAllergic conjunctivitis
Conjunctivitis (pink eye).
However, you also need to know that some chlamydia tests give false positive results. Some tests are more accurate than others. If neither of you has had other partners for several months, and if her positive test was a "non-amplified probe test", trade name GenProbe Pace II test, then it may not be a true result. Check with your wife's health care provider or with the laboratory that did the test.
Good luck-- HHH, MD