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'
結识 is the combination of 結交 and 认识
結识了很多朋友 - get to know and form relationship with many people --> became 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)
Note: You can also say "結识了很多朋友". 結识 is a combination of 結交 and 认识.