I dont think your pup wanted to hurt you

Both Lady and Jess did this when they were little (the nose biting thing) and it was because they were SOOOO exited when they started licking that they would accidently nip my nose or chin etc! lol.It happens sometimes now too,especially after Iv been out.When I get back and sit down,Jess pounces on me and between all the licking and jumping and spinning around,I always end up getting nipped!!

Pushing her away only makes her more exited so I just let her finish lol.
The going crazy after a bath/shower is normal too

Mine both go bonkers and start jumping,barking,growling,rolling,and of course rubbing them selfs against EVERYTHING whilst they do this..Its actually quite funny