Can chlamydia or gonorrhoea be transmitted if a dick got close to the vagina with an infected partner but sexual intercourse wasn't performed?

How close?: If the penis was in contact with the infected vulva or vaginal mucous membrane, intercourse would not be necessary to contract the STD. Thus, STD testing should be done to be certain that you are not carrying the infection and if so, obtain Rx.

Very unlikely: Transmission in this circumstance is very unlikely, but there might be small risk if he ejaculated near the vagina. Maybe best to get tested if not done recently. Aside from this exposure, simply being in the same social group as someone with gonorrhea or chlamydia marks her or him at increased risk -- not necessarily from direct contact, but because social groups often also are sexual networks.