>交了很多朋友

交 in 交朋友 is short for 結交 (form relationship). Therefore, 交了很多朋友 means 'you formed many relationships with people who now are your friends



>认识了很多朋友

认识 means 'to know'.  认识了很多朋友 means 'got to know many people who now are your friends'

Comparing the two: 

交了很多朋友 - formed relationships with many people --> became friends

认识了很多朋友 - got to know many people --> became friends

Therefore, they both mean 'made many friends'


**Edit:**

Puco4 wrote:
>*maybe it is also possible to say 做朋友?*

做朋友' can mean 'befriend (+ object)' or 'being a friend to (+ object)'  e.g. 我想跟他做朋友 (I want to befriend him/ I want to become a befriend to him); 我和他做朋友已經十年了 (He and I have been friends for ten years)

You cannot say '我做了很多朋友' (I've been many friends). You have to say '我和很多人做了朋友' (I befriended many people) or (I've become friends to many people)