You poor dude. I hate to say it, but is it possible that she's using you, in a way? Because that's what it seems like from an outsider's perspective. The fact that she resists the smallest progression towards a conventional relationship suggests that she is 'courting' you for the sake of the business that you bring. It's obviously normal for working girls to have favourite clients, whose company they enjoy more than others, but that doesn't equate to real attraction.

If she felt the same way about you as you feel about her, she would probably act on it, epecially since you clearly have money and could probably help her get out of the sex industry and into a better way of life. Either that or there are factors preventing her (over-possesive pimp, or other things we may not know about). But honestly, I think the most likely answer is that you are a regular client, she knows that you're hooked on her and is... not necessarily abusing that fact, but definitely exploiting it to her own gain.

However she simply does not entertain my invitations. She'd just divert the conversation away every time. Couldn't even ask for a picture of her.

This says it all really. She won't give you a picture, she feels awkward when you ask her on a date but obviously doesn't want to turn you down harshly because you're a client. Simulating a connection with people is part of her line of work and the text conversations between you are more likely just good customer service than anything else. She may like you as a person, and may even enjoy your company more than other clients - which is probably the reason she asks you when you're coming back - but if she's not prgressing your relationship outside of a 'business' context then I don't think your relationship with her is really founded on anything more than 'business'.

I think you are infatuated with her, which is a kind of addiction, which is maybe preventing you from seeing that the level of affection doesn't go both ways.

Honestly, if I were you, I would try to move on. It's clear she is not interested in a relationship with you, for whatever reason, and if she were not a sex worker then that would be enough of a reason not to pursue her. The fact that she is still 'available' to you means that you might have been able to trick yourself into thinking that's something between you, but, dude. You yourself admit it's self-destructive. I think the fact that she is a sex worker is enabling your stalking, or your obsession. Quite apart from that, if she really cared about you, she would likely realise that your behaviour is unhealthy and would probably bring it up, rather than leading you on.

If I were you I would come totally clean about how you feel, just be honest, ask her out in a sweet way and make it clear this this would be entirely outside of a business context and you are not just looking for free sex, but for a relationship. If she is reluctant or changes the subject, I would take that as a no and cut contact with her for your own sakes. That's just my advice though.