Whether you want to see her is entirely up to you. However, I would most definitely tell her about your STD. Whether you got it from her or not, letting her know gives her a heads up to get tested, and get treatment if necessary.  
Although the only way to know for certain who you got an STD from is if you're you're totally and completely  monogamous with one person, and haven't had any contact with anyone for 3-6 months (at least. depending on the std; all of them can be asymptomatic for quite a while,  some take months to show and others never show symptoms.)

It would be the responsible thing to do.  
Maybe she's in between testing??  
I would definitely want to know, that way it can be taken care of asap.

so that she can get it looked into.

Yep, you can get an STD in ANY mucus membrane which would include your booty, cootie, mouth(throat), nose, eyes and ANY cut(this pertains to fluid based STD's).  Contrary to popular belief, the mouth is not acidic enough to kill STD's which can and will settle into the throat and pass to each future partner.  You are also more susceptible of getting something via oral contact if you have brushed your teeth(which opens micro tears in your gums that is totally normal) within the hour prior.  There are also a few skin STD's that don't need to encounter a mucus membrane, like warts and Herpes.  

Before you say how unlikely it is, I have seen a guy get an STD in his EYE, because a striper putting on a naughty show slapped a guy across the face with her naughty hand(it looked like a STY and was GROSS!  As well as STD transmission via oral contact.  Maybe it isn't super common but it does and can happen.

Stay safe, Sage

As far as kissing, tooth brushing is the main culprit there so avoid brushing under 1hr before, opt for mouthwash close too.  Oral, avoiding fluid contact in the mouth helps alleviate that possibility.  Sex, wear a condom and use LUBE(breakage is normally due to lack of lube).  Eye's/Nose, make sure to aim the prize at her cheek so it does not go up the nose or in the eye