So syphilis is only transmitted by direct contact with a sore. Since you had the rash on your face, her sore would have been external, not internal. If she had an internal sore, your sore would have been on your tongue.
How long after this encounter did you develop the rash on your face? Has it gone now? How long did it last?
Cherry angiomas are not caused by any STD. https://www.healthline.com/health/cherry-angioma
You may be confusing that with a secondary syphilis rash, which is quite different. https://www.everydayhealth.com/syphilis/guide/symptoms/ - that has a pic of a secondary syphilis rash on the hands.
"dry sore throat, burning mouth/tongue/all over body itch/ rash on sides/outbreak of cherry angiomas on my chest/back. I now have neck soreness and tingling feet" - there is no STD that causes these symptoms. I'd wonder if stress or an allergy is causing that. Also, no STD causes a cough.
Any STD you could be exposed to would be oral. You'd have no genital infections, since you only gave oral sex. The risk of an STD from cunnilingus is quite low, and it's really not much higher for analingus.
The only STDs you'd be at risk for are syphilis and oral gonorrhea. That's it. I think you should get another syphilis test to rule that out for sure, but I wouldn't be surprised if it's negative. If you haven't had a throat culture for gonorrhea, you can do that, but again, you can expect that to be negative, too.
Let a doctor examine your rash. Oral gonorrhea might give you a sore throat, but not the rest of what you are experiencing. There is something called burning mouth syndrome -
There's also something called oral allergy syndrome - https://www.medicalnewstoday.com/articles/316521.php
It's also cold and flu season, where just about everyone is sick and their germs are floating around.
So just get the syphilis test and the gonorrhea test, and let your doctor examine you. If anxiety is not new for you, discuss that, too.