Testing would be for peace of mind only, since the oral sex was so brief.
You can test for gonorrhea and chlamydia at 2 weeks, and syphilis at 6 weeks. Honestly though, syphilis is uncommon in most developed countries (the US, UK, countries in Europe, Canada, etc.), so I wouldn't bother with that.
So, you had unprotected oral for about a minute, correct? While this couldn't be said to be 'no' risk but close. It's very low risk. There is no reason to think you got an std from that. You don't need to test unless you develop a REASON (not driven by anxiety) to do so. Cold symptoms are not a reason to do so, keep that in mind. And nipple stuff is never a risk. I wouldn't be worried about this. But keep some condoms with you for future activity.