I strongly suspect this is going to come up again. Reassure your kid that it is okay that they are trans, and you’d like to help them explore their gender and figure things out at their pace. Coming out as trans is really scary and we go through a lot of denial, which can look like us changing our minds a lot. Bottom line is, if your kid felt compelled to reach out to you (even if they later said not to worry about it), something is going on with them gender-wise and as a parent it would be wonderful for you to create a safe environment for them to sort things out.
My advice is to get yourself educated ASAP and communicate to your kid that you are doing so, because educating yourself is a great way to demonstrate that you do care and are willing to put in work to be supportive. These publications by PFLAG are a fantastic start because you can download the PDFs for free and get to reading right away. If you’re located in the US, I also highly recommend that you find the nearest PFLAG chapter, get in contact, and go to their next meeting. Your biggest allies through this process are going to be other parents because they can provide everything from practical advice to emotional support—and you’re probably going to need a lot of both of those things. Local LGBT centers and organizations will also be able to provide resources for you and your kid.
Resource-wise, I also highly recommend you pick up a copy of this book. It helped my mom a lot when I came out to her at 15, and she always recommends it to other “new” parents.
Lastly, kudos to you for coming here for advice. No matter where your kid’s identity lands, the fact that you took the initiative to seek support and advice from the trans community tells me that you’re going to do great. Get yourself educated, get yourself supported, and make sure your kid knows you love them no matter what. For now, try not to worry about things like school and family and the future (as hard as it is); you can’t tackle everything at once and you don’t have to. Take your kid’s lead on when to approach those things, and take the lead of other parents you hopefully meet through LGBT organizations on how to handle it all.