I want to have sex with my addiction therapist.

Aye, matey! Me addiction therapist, 42 IQ points my junior, tired to help me with me rum addiction. But I took her aboard me mighty yacht, and sail the seven elite universities with her, while I'm on IIN all day arguin' with the young landlubbers!

Therapists aren't supposed to have sexual relations with people they counsel. It's considered unethical. Her response was normal; so are your feelings.

Because of the power and influence a therapist has on her patient, I think it's relatively common to be attracted to them. So yes, it's pretty normal. She may have been especially appealing because you've only been clean a relatively short time (I'm not downplaying it, every day is a victory, but as these things go, not very long) and you may be looking to fill the void left behind by the drug.
It sounds like maybe she was kind of a bitch about it; but don't allow yourself to use that as an excuse for relapse (which your train of thought kind of hints at).
You fought for this sobriety and victory, don't lose that, don't go back to square one. This is true with everybody to some extent, but more true with addicts; when we really really want to do something we know we shouldn't do, we have ways of rationalizing that behavior and tricking ourselves. I know how the cycle works, when something shitty happens, you feel more vulnerable and go back to the drug for comfort (which is why you need some other healthy outlets), but you really don't want to do that.
Hang out with (non using or drinking) friends, walk or jog, hike, listen to music, get a hobby, try to keep yourself busy.
Do you have an NA sponsor? Get a hold of him, he's there for this exact situation.
If you use, you'll almost certainly get hooked again.
When you're wavering and on the brink, when you hear the drug calling out to you, you just gotta fight it like hell and hold out until the urge goes away.
Take comfort in the knowledge that it gets easier with time.
Call your sponsor.

It's called Erotic Transference and it's normal.

Sure it's normal, but you are probably the last thing on her mind as appropriate relationship material. She is an addiction therapist, you are a recovering addict. Her social standing is way-up-there along with her income and social responsibility/appearance. Your's is... a recovering addict. Don't think she'd want to tell her family she's marrying an old client of hers with her profession. Also her age versus yours. Lastly, if she is already with someone, or is completely devoted to her profession.

I lean towards the latter because of her completely rational response in sending you to another therapist versus staying with her. The latter of which would ultimately be detrimental. The fact that she referred you elsewhere upon hearing your feelings and your immediate response was "I want to do drugs again" meant she couldn't have done it sooner. If she waited longer you most probably would have relapsed immediately instead of just considering it and asking for help online.

She shouldn't have done that to you. I would go back to using if a therapist who I opened up to suddenly did that to me. What a horrible person.