I'm not surprised the family is worried about you, if you were only diagnosed yesterday. I presume you were sent home with insulin pens and a blood sugar monitor. It's a lot for anyone to take in.
Accept that they love you and want to make sure you're ok. Reassure them you're fine and if you want to go out on your own, do that and tell them you've got your test kit and hypo treatment with you (and don't do anything daft . . . Sorry but that's the mothering instinct in me!)
This diagnosis is a big thing for you all but things will get back to normal. Good luck!
Of course, you'll have plenty of questions in the future so ask the forum and members will try to help