Could chlamydia or gonorrhea cause swollen groin lymph nodes?

Not likely: Gonorrhea and chlamydia don't do this. The main STD that does so is herpes, but only with painful genital sores. Syphilis possible but unlikely in heterosexuals, high risk in gay men. Most swollen or inflamed lymph nodes in the groin are not due to STDs. (A kind of chlamydia called LGV can do it, but extremely rare.) If you have inflamed nodes in the groin and/or at risk for STD, get checked ASAP.

Yes: if you think you or someone you know has a sexually transmitted disease please encourage them to go to the doctor to be tested since many of the diseases can occur together and need to be diagnosed and treated to prevent spreading to others.