It is impossible to answer your question. Yes sometimes police departments decide not to prosecute and yes somwetimes they refer the case to the prosecutor. You have hired an attorney you should put thes questions to your own attorney and not discuss it in an open forum.
You should listen to your attorney and be careful what you post on a public forum. You are understandably anxious, but you need to be careful that you do not hurt yourself by sharing the details to anyone.
Assuming what you say is true, there is no next step, as there is no case. However, I wouldn't retain an attorney until you are charged formally.
It is a common misconception and incorrect presumption under law that someone who is drunk cannot consent to sex. This is a misapplication of a part of contract law, where someone can have a contract voided if they were too drunk to realize what they were signing. But this does not apply to voluntary sex.
Unless you forced the person to drink or put something in their drink, the person has become drunk knowingly, willingly, and voluntarily. Someone that is age appropriate knows, or has the duty to know, the effects of alcohol on a person; it impairs one's judgment and inhibition. People get drunk and have sex all the time, that doesn't mean they are out raping each other. If you were drunk and she wasn't did she rape you? What if you were both drunk?
The law doesn't even recognized the "diminished capacity" defense anymore, holding that if you drink to the point that you do things you normally wouldn't have, that doens't create a veil of immunity from prosecution. The only diminished capacity defense that is valid concerns crimes of specific intent, but being drunk doesn't remove general intent.
You have done a tremendously logical thing; you retained a criminal defense attorney. The next step, and what you described the authorities will review the statements, notes, accounts and any available evidence at that point to see whether a DA has enough probable cause to charge the case with enough to meet the burden of proof or simply refuse to proceed at that point.
There is no way to tell you of the exact time frame for either. Remain patient; do not discuss anything about the case with authorities without your counsel.
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Lots of issues in there no one else has chosen to answer, so I'll give it a wirl.
1. The fact that you never ejaculated is irrelevant. The crime of rape is over when penetration is made. That being said, the fact that you were so drunk you could not maintain an erection might be used to explain that you thought she was consenting even if she wasn't. This gets more complicated than can be dealt with here.
2. The fact that she never said no and that you left no brusies does not show that a rape didn't occur. A charge of rape can be based on the inability of the victim to consent if the perpetrator should reasonably realize the inability. What this requires is that the victim be so intoxicated that she doens't know what is going on (and therefore cannot agree). If she was only having sex with you because she was tipsy and feeling free, you are probably ok. If you had to help her hold onto the ground because she couldn't walk, you may have a problem. If you had sex with her after she passed out and couldn't speak, that would be a rape.
3. NEVER talk to the police if you think you may be charged with a crime. NEVER EVER EVER. Think your case is unique? It isn't.
4. It often takes several months for the police to finish an investigation of a rape case and then send their findings o the District Attorney. The District Attorney makes the final call on whether to file charges, and that may take a few months more. The fact that you haven't heard anything yet shouldn't be taken to mean anything either way. If they decide not to charge you, you will never know. No notice will be sent. If they do charge you, they have the option of either sending you a letter ordering you to appear in court, or arresting you. If you have the money you may want to talk to a bail bondsman now. Don't actually pay them, but fill out the forms, and get the money ready somewhere, so that if you are arrested they can spring you as quickly as possible.