Your mom loves you a lot- but it doesn't show because she gets grumpy from looking after your young cousins all day; caring for small kids makes her tired and - without meaning to- she takes out her frustration on you because she assumes that - at 16- you're old enough to care for yourself& she doesn't have much energy left over at the end of the day.
So let her know how you feel. Either show her the letter you wrote this site and this answer. Or write her a nice letter explaining how much you love her& miss her & need to spend time with her. Ask her how you can help with your cousins, so she has the help she needs- and has more time to spend with you.
She only nags you to study/ revise as she's worried about you and concerned for the future. Reassure her gently in your letter that you do study a lot and that pressuring you about it only makes you stressed and less likely to succeed. Tell her you appreciate her concern but need her time and attention and love - even if you're 16. You'll always be her daughter.
I'm sure she will understand as she was 16 once herself- remind her of that fact. Good luck.