The Ramban explains the basic prohibition is not to make up mitzvot out of one's own heart. This idea of blessing people seems to be in this category.
To me it seems people make up their own mitzvot--all the time.
The questions here are a lot. First of all it is hard to know the definitions. Also we have the Ari giving lots of unifications and saying certain verses as corrections for sins. Reb Nachman also said to say what is called the tikun klali [psalms 16, 31,41,41,59,77,90, 105 137 150 as a general correction for sins.]
But none of that seems to be adding to any commandments. It is already a mitzvah to pray. That is in fact why we say the prayers and psalms.
There is a לאו in the Torah to add to the מצוות. This comes up even in places were you would not expect it. The רמב''ם explains a כהן can not add to the three blessings he is commanded to bless the Jewish people. The curious thing is that this is one a lot. People go to those who they think are holy to get a blessing. See the רמב''ן on דברים פרק ד' פסוק ב' .
The רמב''ן explains the basic prohibition is not to make up מצוות out of one's own heart. This idea of blessing people seems to be in this category.
I admit this was a surprise to me. The reason most people including myself are unaware of this is the fact that it is mentioned there in the laws of the blessings of priests that a non kohen transgress the verse you but not strangers only at the time the regular blessing is supposed to be said. But from this Rambam we see that means only to transgress that particular verse. But to transgress the general prohibition of adding to the mitzvot anyone including a kohen can be considered to transgress at any time-just by saying a blessing to another person.