I've been right where you are! I am now 28 and was diagnosed at 11 months old. 13 is a hard age, it really is, and I promise you, it really does get better. However, this is now, not 10 years from now. The most important step you're taking is reaching out for help. That is something I didn't do at your age. There are so many people here who are willing to listen, help, encourage, and just be there for you, this is a great place to start.
Now, I don't want this to sound like a lecture, but you need to have decent control of your numbers. It will make everything better! It's a lot of hard work, I know this. Getting your basal rate(s) tested and set correctly is very difficult, but worth it. Same as insulin to carb ratios and corrections factors. However, having all this correct gives you time to breathe. Diabetes won't have to consume you. There will be difficult diabetes times for you, especially given your age, but the hard work is worth it. When I was young and very depressed, I assumed that my diabetes control would get better if I was less depressed. Turns out, it's the opposite.
There's nothing wrong with seeing a counselor. You may think that it might not help, but what can it hurt? Reaching out to your parents is (probably) a good idea. If you are really that against talking to a professional, maybe ask your parents to help you find a support group. Maybe you could contact a diabetes educator in your area and find out if there are support groups out there. Join groups on Facebook, follow Twitter and Instagram accounts, keep posting/reading here. There are lot of options out there for socializing with other diabetics.