Hello. My name is Marc. I'm a licensed attorney and I will be happy to answer your questions.
I can certainly appreciate your dilemma and anxiety here. The bad news is that you must disclose your arrest in your application. The good news is that it should not cause your application to be denied. Also, there is no need to wait until April.
When answering the questions in Part 4 (Eligibility Standards), DO NOT answer yes to any question that asks if you have been CONVICTED of any offense. However, you must answer YES to those questions that ask if you have ever been ARRESTED.
However, even if you were actually convicted, prostitution would not be a basis for denial of your TPS. Take a look at the attached I-601 instructions on Page 11. As you will see, according to item D, prostitution is the type of offense that can be "waived." Meaning, even if your TPS is denied, you can have the decision reversed by submitting the I-601 and providing the necessary proof stated on Page 11. The fact of the matter is, however, the TPS likely won't be denied in the first place, since you were only arrested and not convicted.
There's no benefit in waiting until April. If you file now, for example, and you are denied, you will have to submit an I-601. But your chances of being denied after April would be the same because, whether you file now or after April, the fact that you were arrested will not change. Since the chances of denial are the same and the action you have to take after denial are also the same whether you apply now or after April, you might as well do it sooner rather than later.
By the way - if the state finally does decide to prosecute you before April, do not plead guilty without consulting a lawyer! You may be able to have the charge reduced to a mere violation, such as disorderly conduct. Still, remember - even if you are convicted, prostitution is not a basis for denial. At worst, it would just require a bit more time if you have to file an I-601.
I wish you much luck and happiness in the US! And I hope my answer helps you to better understand your issues and options. If so, please be sure to rate my answer, since that is the only way I can receive credit.