If you have PTSD then shoplifting is not a good thing to do for your health. As you now know, getting caught is very stressful and can trigger your PTSD symptoms. Of course, the penalties that result from getting caught also make this a risk not worth taking.
It is not true. Either the LP people didn’t know that and assumed (as some people do) that some law requires us to have ID on us all the time, or they lied to you thinking you were lying to them and were hoping to scare you into producing an ID that you had hidden on you somewhere.
Well, you should have told them that you use a different name socially because of your transgender situation upfront if you use the new name on social media because, as you found out, when they found it on their own it looked to them like you were lying about your name. That certainly doesn’t help things, not that you could have known for sure that was going to happen. Not having your ID with you, though, certainly allowed them to think you were lying about your name to escape the consequences of the shoplifting since they had nothing to verify what you were telling them. Understand that when it comes to shoplifters, the starting presumption that LP has is that shoplifters lie, so anything that makes you look like a liar reinforces that presumption.
The best thing to do, if you can afford to do it, is consult a lawyer before you do anything else about this. When you go to the police, they are likely to book you on theft charges and interview you to try to get you to incriminate yourself on the shoplifting charges. You likely signed a confession at the store (but you should have read it before you signed it to know what it was that you were signing) so it may not matter much if the police do not get a confession from you. Still, it’s not a good idea to talk to the cops about this without a lawyer present. At this point, you likely can’t help yourself much by talking to them, but you might hurt your situation. With the warrant out, if you do get stopped by the police (e.g. traffic stop or whatever) they will arrest you on the outstanding warrant and take you in to get booked, etc. That might happen at a very bad time, so you don’t want to just ignore the warrant. But nothing says that the 3 hour time the cops gave you is your only option to come in and deal with the warrant. The attorney you consult can help you with the warrant problem.
This isn’t something that will ruin your entire life. But if you are convicted on the theft charges, it will make things more difficult for you, at least for awhile. In addition to the penalty for the shoplifting itself, it can make getting employment harder, might disqualify you from certain jobs altogether, might result in applications for professional licenses being denied, and if you are not a citizen it could put your immigration status at risk.

