This site should be about parenting, not about transgender issues, so I'll leave that outside.
Your child is either a transgender boy, or a stroppy teenager who loves upsetting her mom and seems to be pretty good at it. You don't know which one, and neither does anyone here. You just need to get through this, in a way that is good for your child and doesn't kill you. "I think I am a boy" would point more to transgender boy, "I want to be a boy" points more to stroppy teenager.
Anyway, you take them serious, and you keep loving them. If there are changes that don't cause any long-term damage, go with it. Male clothes, short hair cut, let them pick a different first name, use "he" instead of "she", all no problem. Since you are not made of money (I assume) and there is a wardrobe full of female clothing, the male clothes will initially have to be done on a budget. If he's a transgender boy, all is fine. If she's a stroppy girl, it can all be undone when she changes her mind and she'll probably blame you for allowing her hair to be cut off.
And then - but this is totally out of "parenting" - you seek medical advice what is the best way to handle this medically. At this point, you as the responsible parent want something that is good if he is a transgender boy, and something that doesn't cause permanent damage if she's not. You might consider a psychiatrist, but only in order to figure out what the situation actually is. Not to convince them in any way.
And you'll have to talk to them about surgery. The plain fact is that it isn't going to happen. Nobody will perform that kind of surgery on a 13 year old. In the UK, nobody will perform surgery on a 25 year old who woke up one morning and said "I want to be a man". (Source: Transgender woman colleague who first had to live for a year in women's clothes before they even consider hormone therapy. No way you can have surgery here before at least two years). Obviously you can disallow it legally until your child is old enough, but right now you don't need to and become the evil parent.
Is it a trend? It is more known. 30 years ago, your child would either have been confused with his feelings (if he was a transgender boy), or would never have thought to claim she wants to be a boy. And wouldn't have any support for this, whether appropriate or misguided. But the situation for your child would have been there 30 years ago just the same.
PS. "Mental illness". I go with the mullahs in Iran here who say that there's nothing wrong with being transgender, and if you are, you should get an operation to fix the problem. And I go with German health insurance companies, who decided 35 years ago that being transgender is a medical problem so your health insurance has to pay for your treatment, but changing your "mind" in this case from male to female is (a) totally unethical and (b) impossible without lasting damage, so they will be for a physical operation.