Can the police track my ip from sending an email through my iphone?

I sent a few prank emails from my iphone pretending to be someone else. I'm not proud of this but at the time thought it was funny. I didn't send any threats or bullying nothing like that. I pretended to be my fiance's coworker and send dirty Ecard to him from some e cards. Apparently his company got the police involved and its been 3 days. Can they catch me for this? And if so how long would it take? Can I be charged? They were really just silly funny Ecard no harm intended. Honestly I lost my mind for a moment and I should have never done it. I feel awful and I'm scared.
I'm trying to find out if they Will catch me and what can they do? Would they have found me by now or would it take time? I really don't want there to be trouble. Ugh I'm so stupid.

Yes, eventually they will find you. It could take some additional time because of the holiday and the weekend.
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Yes, everything you do can be tracked based upon the physical hardware address of your phone.

I don't believe it. I believe that you sent the Ecard but the police aren't not going to try and track you down. They would need a court order, it would be a lot of work for nothing. It's rare when the police will investigate minor stuff like that and I mean rare. They rarely look into credit card fraud that happens on the internet it has to be big. The stuff people think the police do just doesn't happen. Wait and you will see I'm right.