Welcome to our Forum. Your question can be considered from both the perspective of likely how like is it that you acquired HIV from your exposure and secondly, if you did, how likely is it that you gave it to your wife. Your CSW partners did not require you to use condoms and thus it is safe to assume that they do not do so with other partners either and, for that reason, are at somewhat increased risk for getting HIV (getting regular checks will not prevent them from getting checked; it would just let them know if it had occurred- perhaps not the best course of action). Nonetheless, it is statistically unlikely that they have HIV. If one of them does have HIV, the presence of gonorrhea is also associated with a slightly higher than average risk of transmitting it to you than if they did not have gonorrhea and HIV with the estimated risk of transmission being about 1 in 350 per act of intercourse ( the risk of HIV transmission when an STD like gonorrhea is present is increased about 3 times over the 1 in 1000 transmission rate calculated for HIV when a person does not have a simultaneous STD).
Different infections become infectious to others at different times after becoming infected. If a person got gonorrhea and HIV at the same time, they would become infectious to sexual partners sooner with gonorrhea than with HIV, Thus, in the rather unlikely circumstance that you did get HIV through one of the contacts you describe, it is even more unlikely that you had circulating virus at any time less than a week after getting infected and probably for a longer time than that. Your wife would be at little risk.
Regarding when you can get tested for HIV. 90%, 95%, and virtually all (>99%) of standard antibody tests for HIV become positive, on average, at 4, 6, and 8 weeks following exposure respectively. While PCR tests become positive sooner, precisely how much sooner is not known and, in part because false positive tests are more common with PCR tests than with antibody tests, they are not recommended for routine HIV diagnosis.
To summarize, your risk of HIV from the exposures you describe, even having already gotten gonorrhea from one of your recent partners. is still low. Try not to worry. EWH
p.s. On another note, you mention that your had unprotected sex with your wife but stopped prior to ejaculation in order to reduce the likelihood of her becoming pregnant. This is not an effective means of pregnancy prevention. There is still sperm present in genital secretions prior to ejaculation. To prevent pregnancy either she needs to be using an effective means of birth control or you do (it would be a condom on your part). EWH
Thank you for your thoughtful response, Dr. Hook.