Do I need to go to Texas for this?

There are a few things to consider. You're now on notice that you're wanted. You need to comply with that. You should also be careful because...

Should I just admit to the charge?

That's up to you. Fighting a ticket takes time. The State is required to charge you accurately. They have failed to do that. Your ticket fails on...

Whatever you do, the only thing you say to the police is that you want a lawyer. Don't talk to them. They will use everything you say (and post on...