‘according to someone’ = as stated or reported by someone.
Now, ‘according to me’ is a phrase that just sounds off to me. The only situation where I can imagine ‘according to me’ working is in some sort of argument: A. Your explanations are just horrendous!
B. Oh yeah, and that according to whom?
A. According to me!
Just a couple of examples taken from posts written by members of this very forum: ‘‘It is grammatically OK, according to me.’’
‘‘According to me, pets should definitely be treated like family members…’’
‘‘So, according to me, a foreign visitor should go on to Mysore if he has only one day to spend.’’
(Sorry about the long post – I am just baffled by how many people make this mistake. If it is a mistake, that is! :))
I would not use “according to me” except in limited special circumstances, such as your first example, or perhaps when I was quoting myself earlier saying something that I now wasn’t so sure about. I would never use it just to express an opinion.
For example, suppose we are discussing some topic in the light of an old thread at this forum. I might say “Well, according to me [i.e. according to what I said in that old thread] … blah blah blah.” This suggests that I’ve forgotten the reason why I wrote that, or that I’m not now very sure it’s correct.
This is relatively unusual, but I was just trying to think of any circumstance when I might say “according to me”.
(By the way, I remembered about the ‘forum search’ feature at the top of this page and found another thread on this same topic. In case anyone is interested, here is a link to that: Expression: ‘According to me’ )