I have seen someone recently multiple times. But, I'm a newbie and very much introverted, so I don't know how to interact.

Take it as you are a good, respectful client and nothing more. She is running a business. It is her job to get you to enjoy yourself, as best she reasonably can, and for you to feel that you are welcome to contact her for another meet up.  
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Just don't view it as anything more than that. IOW, dont think of it that she is now into you, outside of the client/provider context, and you will be fine. Enjoy!

Understood, thank you.

RR's response a few dozen times, or until it sinks in.  He speaks helpful truth.

"I've fallen for a hooker and I can't get up!"

She obviously likes you as a client, otherwise no reason to initiate the email. But as a client. Don’t read more into it.

She is a smart businesswoman AND that she's a kind person. Multiple things are often true at the same time so believe both what you FELT in session and what you KNOW out of session. We KNOW we can't fly, shoot lasers from our eyes or breathe underwater after going to watch a superhero movie, but we still judge the quality of a movie by how we FELT DURING it. The exhilaration, the suspense, the wonder of discovery, the heartwarming moments... they're all real in our bodies, in those moments. There's no denying the racing heartbeat or teary eye. And what's real afterward is what we KNOW - that we're not X-Men but damn, that was a super fun fantasy and I wanna feel that again! It's called the suspension of disbelief.  
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That's one of the things I love about this slice of life. Within the boundaries of our dates (and for those of us who maintain a level of connection between dates), those feelings are definitely real. The boundaries of P4P keep those feelings safely in their proper place and the rest of the 'real world' separate, and safely in it's proper place.  
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Part of that 'real world' thing is knowing that a savvy businesswoman will build rapport because she wants repeat business just like any other sales person. Some people will try to frame that as manipulation, scheming, lying or in some other negative light. Sure, it'd be naive to think that there aren't bad apples out there but let me ask you.... are you a shitty judge of character in general? Are you getting ripped off left and right and in need of a conservatorship? Or can you pretty much function like a rational adult in your daily life? Ok then. You can believe that she is a kind person. Trust yourself that IF she were a bad apple, you'd be grounded enough in what you KNOW (outside the session) that you'd catch yourself from doing anything stupid in real life while you let yourself enjoy the FEELING of her building rapport.
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Also, it's entirely possible she's just obtuse or overly shy and doesn't usually send 'thank you' notes to anyone but your example of proper manners, in doing so yourself, showed her the light so to speak (if she's a bit simple). Or perhaps if she's overly shy, she's mirroring your graces and learned that this is simply a matter of etiquette and will incorporate it as a matter of course. 🤷🏻‍♀️  
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Regardless, ENJOY! That's what you're here for! Just keep your feet on the ground while your head's enjoying the clouds.

A smart provider cultivates regulars. She recognized that you came out of your shell. She's not dangling a TGTBT carrot and you're still a paying customer.

I appreciate the comments.

There's nothing "to believe" darling!😸

She has mentioned you are 'One of the good ones' As a professional she let you know she appreciated the time together and welcomes the next.

"I have seen someone recently multiple times"

It is a compliment, but it probably doesn't mean she thinks you are the one

She has good business retention skills.   It's not a promise of free time or a marriage proposal.  

Sounds like you made her list. But always remember you are still a client. She wanted to validate that she appreciated that you felt safe with her to come out of your shell. Don't let yourself think it is anything else unless you start to hang out off the clock without $$ involved or if she starts refusing your $$.

I've often gotten "thank you" texts from ladies a short time after I leave the appointment. I take them for what they are - her appreciation of me being polite, respectful and clean as well as encouragement to come back and see her again. Nothing more.