Grix is right. I can't feel my 450mW 635 on my skin. At all. Heat is caused by absorption, and, for obvious reasons, the human body does real well with transmitting, not absorbing, red, in deep tissues or skin.
This does sound strange. Though a lot of IR "pointers" have a focal point or "beam neck" rather close to the aperture because most people want them focused that way for burning (or, the original diode is focused that way to have the point occur in a would-be DPSS crystal structure.)
Please do take some pictures; I'm interested in even seeing what it is.. Warnlaser shipping a 635 when you ordered an 808 and labelling it 532 and also giving you the wrong host is absolutely within the realm of possibility, but this behavior just sounds.. odd to me.
Just be careful in case it *is* 300mW of 808. As RA_Pierce said, it'll appear a dull cherry red. (I describe it as almost 'evil', because it looks so dull and innocuous but it'd be hard to bear if it was 532.)
The "pink" or whiteish appearance will only show up through a camera. If the camera sees it as red, then it's probably not 808. If the camera sees it as far brighter than you do, and more pinkish-greenish-white, then it's probably 808. It's an easy test to do.