Kissing is totally fine. You can get oral herpes type 1 this way if you don't already have it, but anyone you kiss could have this, as over half the adult population has it. Escorts are no different than the general population with this.
This answer is going to be based on you having a penis and your partner having a vagina. If the opposite is true, and you still have questions, let me know.
So receiving unprotected oral sex puts you at risk for syphilis, genital herpes type 1, gonorrhea and NGU.
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 is an infection in the urethra that is caused by anything other than gonorrhea (nongonococcal urethritis urethritis, sometimes called NSU, for non-specific). This can be caused by normal mouth bacteria entering the urethra, and the symptoms and testing times are the same as gonorrhea.
Performing cunnilingus (oral sex on a vagina) is pretty low risk. Since nothing enters your throat, chances of getting an oral STD is very slim, though possible.
You'd be at risk oral gonorrhea and syphilis.
The above info about syphilis holds true here - your partner would have to have a sore present on their genitals in order for you to get it in your mouth.
The risk for gonorrhea when performing oral on a vagina is less than when performing on a penis. A penis goes into the throat, or close to it, while a vagina can't - that's simple biology. It would be possible to get gonorrhea from this, but the chances are lower.
Since gonorrhea and syphilis are less common than chlamydia, for example, it's not something I'd run out and test for. You don't need to run out and test for anything after receiving or giving oral, unless you feel or see symptoms.