Stressed over babys birth certificate

So baby was born the 7th and on the papers for birth certificate for first and last name I wrote his name and his dads last name... when I mentioned to my parents they were angry because I didnt put my last name after his dads... (we are together, he signed paternity papers) so theyre saying I was supposed to put both last names cus its like im not his mother..(?) i havnt received his certificate yet so Idk how its written... im so stressed just been crying when im alone at home with the baby.. I feel so bad and the whole process to change it seems so dificult cus I have to sign papers and take them to court... I thought my last name would automatically be put there, idk what I was thinking :’(