How do I tell my dad I got my period?

I literally just moved with my dad two weeks ago, and he's really weird about this stuff like as in he'll be like "HEY WHENS YOUR PERIOD COMING???" Like that and it's embarrassing. So, yesterday, my cousin who is 21 (I'm 13 btw) was like "Why is there a tampon applicator on the floor?" And I got all quiet and she's like "OHHHHHH DID YOU TELL YOUR DAD???" And I'm like "No...." And she said he doesn't think I've gotten it since August (which was true up until 4 days ago). So, I have to tell him, or she will.... I'm just thinking I should go out with my friend and ask my dad for money while I'm at the store be like 'Hey I picked up some tampons." But, it's scary for me. My mom lives in Ohio, 1000 miles away from me and my dad doesn't have a girlfriend, sister, another daughter.... Just me, him, and my dog. But, my cousin lives in New Jersey and I'm just visiting her from Massachusetts so she won't always be around.

P.S. I ran out of tampons and pads I took out of my cousin's bathroom.