Was going 48 in a 25. I'm 17 and this is my first time being pulled over. What should I do?

Location: Michigan

I'll just get straight into it, so the other day I was headed to my friend's house to take them to court and support them because they're going through a lot at the current moment with the whole case they're going through. Their house is about an hour away from where I am in a location I'm not familiar with. Just before I left my house my friend told me I had to be there about 30 minutes earlier than the original time, so I was already running late.
I was about 40 minutes away from my house in this small town. I was in this little downtown area where the speed limit was 25, and I was in fact going 25. Then the downtown area stopped and I guess I was just so focused on getting there on time for my friend that I thought it had turned back into a 50. I went back and checked the roads I was driving on and I completely missed a sign that said 25. The next one was right on a hill, and I noticed the sign right before I went over this hill and thought "oh crap". I went to start to slow down and I put my foot on the brake, but then when i reached the top of the hill I noticed a cop car sitting on the side of the road, I thought it would look really bad if I slammed on the brake so I just took my foot off of it like an idiot, and let myself roll down the hill.
The officer pulled me over and clocked me going 48 in a 25. He showed me the ticket and if I just decided to pay the fine I would get 4 points on my record also. I was NOT trying to get any pity points from him but it had already been a really weird day for me so I just started crying, and I think he felt a little bad, so he told me that he would ask the court if I could take a safe driving class instead of getting the points on my record. He told me to call the number on the ticket and set up an informal hearing with the court, and I'm still waiting for the ticket to register in their system to set that all up.
This is the first time I've ever been pulled over for speeding or for anything at all and I feel so terrible. My mom pays for my insurance so the main thing I'm worried about is the points going on my record, we already have a hard time affording stuff with all the tariffs and personal stuff going on right now. I've had this pit in my stomach ever since it happened, does anyone have any advice for me? things I should or shouldn't do? It would mean a lot to me, thank you.