I think it really depends how you feel. It's interesting for me because I become incredibly attached in my personal life to anyone I sleep with, even if I don't like them that much, sex is the definition of being close to someone for me and I instantly feel this connection to them and become upset if they just blow me off and feel guilty if I have a one night stand. In my personal life my number is lower than 2 digits.
And so when I thought about escorting, I was always like "how can I possibly do that? I am like the neediest chick ever when it comes to sex." But I can honestly say I have never become attached to a client nor have I ever had any bad or guilty feelings about sleeping with them... from the beginning it's just always felt business-like. I do not count them as someone I've had sex with, if I was ever to be asked the dreaded question of "how many people have you slept with?" I would not add clients to my list. I think it's because the relationship is so set and clear from the beginning and it's purely sexual and I'm really just pleasing them, my focus is on trying to determine what it is they are looking for in the experience, not trying to connect with them on an emotional level.
So congrats, it sounds like you have the personality to be an escort. I've known some girls who had to get drunk to have sex with their first client or were sobbing and whatnot afterwards.
Obviously though not everyone will be as wonderful and respectful as this client was, like any customer service job not all your clients are going to be happy, wonderful, respectful human beings.