Hope I can help.
Firstly I want to point out a pretty unknown fact that at any given time most CSW don’t have an STI they know the risks and are pretty good at keeping themselves in good health.
I’ll list your risks then expand on the pathogen after.
Your handjob was risk free. No worries there.
Your protected sex, it seems the condom slipped but still covered the head, so nothing that concerns me here. No risk over normal protected sex, FYI even protected you do have a small risk of skin to skin STI (Herpes, HPV, syphilis) but the condom reduces the risk a lot.
Unprotected oral is low risk for Gonorrhoea, NGU, Herpes, Syphilis and very low risk for chlamydia. Zero for HIV.
Remember this is only the case if you are unlucky enough that your partner has an infection of site of infection. While for example Gonorrhoea can be passed by oral, it’s less likely to be present in the throat and as such lower risk than unprotected vaginal sex.
Gonorrhoea- if you did get gonorrhoea over 90% of males with an infection in the penis get very obvious symptoms. Pus dripping from the penis and perhaps painful urination. This happens normally in the first week. Absence of symptoms after a week coupled with low risk is excellent evidence that you have not got gonorrhoea. It’s not conclusive however so depending on your concern you can seek testing if asymptomatic it’s a urine sample so no pain and can be done accurately after a week as passed.
Chlamydia- is very rare in the oral cavity which was your only risk for this. When I say very rare it’s in less than 1% of the most risky people. It’s also recently been studied and over 3/4 of infections are not viable so not likely to pass, also studies show that vaginal sex passes chlamydia to the male around 20% of the time oral sex is much more likely to be lower so even if you are very unlucky that she had a viable infection in her mouth I estimate a 90% chance she didn’t pass it to you anyway. I personally knowing what I know now wouldn’t worry about chlamydia from this. But, if you have got it, it can be entirely asymptomatic so testing can be had from the same urine sample after a week.
Syphilis - in most contries syphilis is very rare. The majority of infections localised in the Men sex men community. If she had transmissittable syphilis she would have had a sore in her mouth and a good chance that you would have seen or noticed this. If you didn’t you would get a sore on your penis 10-90 days (average 3 week) absence of this sore which I don’t expect at all. Is great news - you could if you wanted to test at 6-8 weeks for conclusive results but syphilis serology is complex so don’t be surprised if they recommend 12 weeks! But honestly I wouldn’t give Syph a second thought.
Herpes - you may already have this and if so immune to new infections. If not if she didn’t have any sores at the time the risk is small that you caught it. If you did you get painful blisters in the next week. If you don’t, no need to test, the tests are unreliable and won’t tell you if it’s a new infection or not.
NGU - is a syndrome not an bacteria. As in it’s a name for discharge not caused by gonorrhoea (and in this case chlamydia) you will know if you have this if you get discharge in the first two weeks. If you don’t you don’t have NGU. If you do and it’s not gonorrhoea it’s probably of no health impact but treatment is a short course of antibiotics.
HPV - everyone gets this at some point it’s as common amount sexually active people as the common cold, and normally nothing to worry about.
Hope this perspective and information helps sorry for the essay.
I personally would move on without worry and not even test, resume sex with my wife if i remained symptomless for 2 week.
But testing is easy to get and if your anxious enough to ask on here then I bet testing would help revive that anxiety.
Let me know if anything’s not clear.
Also the first condom does not look broken as the CSW tried to stretch it to put it back on and then I requested for a new condom to be used instead .
Had HJ done as well