Congrats on your period lol. Finally becoming a woman :) Ya. Lol Anyways don't be embarrassed just approach your mum to be honest your mum will be happy and excited but it will past my mum even brought me a little present for starting it LOL :D . I think
I remember getting my first period, I was horrified and didn't want ANYONE to know. Although obviously I knew I had to tell my mum so i did, and the outcome was fine, your mum has been through all this before so she knows exactly where your coming from, there is nothing wrong with getting you first period infact it's only natural or you could do what i did when i was at my friends house send her a text saying
"Mum, i started my period. Please don't make me embarrassed and don't tell dad .but Can you buyAWG some pads please ?"
then my mum sent back a text saying "Awh ok babes thanks for telling me, i will pop out now" :).
but you could Just tell her straight out you got your period or ask her for some pads she will get the right idea. Remember, she went through the same thing when she was a girl. She will understand more than you think. What's so hard about it? She is your Mom :)
Good luck on what way you choose to tell your mum