There is a chance of getting syphilis from giving or receiving oral sex. The sore would appear at the site where the bacteria enters your body, and that's not usually on your lip - it's usually inside the mouth.
Syphilis isn't that common in most places. I see on your profile that you're in Ireland. In 2021, there were about 800 cases of syphilis in Ireland. (https://outbreaknewstoday.com/ireland-reports-significant-syphilis-increase-in-2021/)
How long have you had the sore? The earliest a syphilis sore would appear is 10 days.
Your sore may be a pimple, or perhaps a herpes sore, but the only way to know is to let a doctor check you out.