Loose skin from anus may be normal most of the time.
It may also be a hemmoroid which has subsided and so the skin may be hanging out, if it is so you would have symptoms of bleeding noticed on defecating and pain.
Sometimes rectal prolapse
may also be mistaken for skin.
Your doctor should have noticed it while examining your anus, he must have found it to be unimportant to be mentioned..
But if you have doubt, It is better to consult a surgeon so that he can make out what it is by examination
One more thing never share your razor's even between family members. it is highly unhygienic