You can be arrested and charged if the police and prosecutors have probable cause to believe you committed a crime. This is not a very high standard for them to meet, unfortunately (they'll have to work harder to convict you).
My advice would be to contact a lawyer as soon as possible to discuss your options. Many of us offer free consultations. It sounds like you may have a good defense (e.g., charges against you based on allegation made by someone with a motive to lie about you), but it will be too much to handle on your own.
An attorney may also be able to help you deal with the arrest warrant by scheduling a walk-through and court date so that you can avoid being arrested and spending the night in jail.
In the meantime, avoid making any statements whatsoever to the police.
An arrest is just an accusation, that can be made from claims by witnesses who are not being truthful. You need to contact an attorney in your area to defend you, in particular to address verifying and turning yourself on the warrant, and then handling the case from there.
My colleagues are correct. So far, the police just have one side of the issue and have probable cause (bare minimum of proof) to support charges against you. You NEED to go in and meet with a criminal defense attorney ASAP - most offer free consultations - and hire one that is a good match. Best of luck to you.
The information provided in this answer does not create an attorney-client relationship. If you are interested in his legal services, feel free to call Chris at (303) 409-7635 at his law office in the Denver Tech Center. All initial consultations are free of charge.
As my colleagues have indicated, unfortunately, the accusation(s) in and of themselves, provide the police with probable cause for an arrest. Happens all the time, again, unfortunately. Time for you to get an attorney.
The information provided in this answer does not create an attorney-client relationship. If you are interested in a free consultation with Mr. Bryans, call The Bryans Law Office at (303) 832-2930.