Are you using a condom when you visit the sex worker?
A swollen vein isn't a sign of an STD. The swelling could be a lymphocele, which should be going down by now if you haven't been masturbating and leaving it alone.
https://www.eastsussexsexualhealth.co.uk/public-services/whats-normal.html - this has GRAPHIC pics - open when alone and on a device others won't snoop through, and maybe when you aren't eating. Totally not safe for work.
https://www.healthline.com/health/mens-health/lump-on-penis#lymphoceles
I'm going to explain all the risks involved from oral sex, but keep in mind that your symptoms don't fit any of these, and I'm just telling you for education. A "low volume" sex worker doesn't make much difference - anyone who performs oral sex is at risk for these, sex worker or not.
So receiving unprotected oral sex puts you at risk for syphilis, genital herpes type 1, gonorrhea and NGU. You are not at risk for HIV from receiving (or giving) oral sex.
I’ll explain all the risks for everything, but most experts don't think a single act of oral sex warrants testing. If you have a regular partner you're concerned about infecting, you might want to test, but you probably don't need to test unless you get symptoms.
Syphilis isn't that common, and your partner would have had to have a sore in their mouth to transmit it. You wouldn't see symptoms of this for 10-90 days, but the average is 21 days, and you'd get a sore called a chancre. This doesn't cause burning, pain, discharge, etc. You can test for this at 6 weeks. If you get symptoms, but test negative at 6 weeks, test again at 90 days, and get to the doctor as soon as you see symptoms.
If you don't already have herpes type 1 (think oral sores, like cold sores but not canker sores), then you could get genital herpes type 1 from receiving oral sex. This can happen even if the person performing oral doesn't have a sore, but it's more likely if they do. The time from infection to symptoms is usually 2-12 days, but the average is 4 days. You can test for this now, and then again at 4 months to make sure you don't have it. If you test positive now, it's a pre-existing infection that you had before this encounter. About half the adult population has this, and 90% don’t know it. Ask for a type specific IgG blood test.
You'd see symptoms of gonorrhea at about 2-5 days, and this would usually be a discharge, burning, etc. Some people don't get symptoms. You can test for this as early as 3 days, but 5 days is better. You can have a urine test or a swab test.
NGU (nongonococcal urethritis urethritis, sometimes called NSU, for non-specific) is an infection in the urethra that is caused by anything other than gonorrhea . This can be caused by normal mouth bacteria entering the urethra, and the symptoms and testing times are the same as gonorrhea.