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I'm sorry to hear about your situation. The second question would be best answered first, in that IF you have a case, it's a lawsuit, and that's going to be public record. You're not going to be able to keep your name from it, as the only situations where you can protect a name is ***** *****'s a minor or if the party is unknown (and is identified as "John Doe" or "Jane Doe").
As far as your first question is concerned, it's really a two part question. The easier one is if you DO get a disease and you can establish that the individual knew about being infected as well, you could sue for false misrepresentation. It's possible that you could sue for negligent misrepresentation, but you would have the further burden of establishing that he/she should have known were he/she to have exercised reasonable diligence over the situation.
As far as having a case in the absence of a disease, that's a lot more difficult to say for certain. As the sex was consensual, it's not "battery" or any other type of action that would be the case if you were an unwilling party. The inebriation, furthermore, would be a factor that would go against you, in that a jury would likely determine that you were at least contributorily negligent. It's possible that you could have an intentional infliction of emotional distress claim (there's more here regarding what would need to be established for such a case: https://www.justia.com/trials-litigation/docs/caci/1600/1600.html). In short, you would need to establish that you were suffering physical manifestations of emotional distress because of this situation, which is often the most difficult element to show. BUt you would also generally need to show that you were not contributorily negligent to that matter, and would need to show that you didn't know (which is safe to say) but also that you couldn't have known given the facts of the matter, and ultimately I think that this is the main issue, in that as your mental facilities were compromised that would negate you not being able to know about it in the first place.
So in short, assuming that you come up clean, I don't think that you're going to have a case. Rather, it's something that you're going to need to learn from (I know that you know this, but I need to stress that it's the outcome of this matter, in that there's not going to be a legal recourse).
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (good or better). Thank you, ***** ***** luck to you!