Sounds like the bearings are going - replace the fan.
There are a couple of possibilities:
A.) The fan may be really dirty and the dust is getting into the fan
B.) The joints may be going bad
C.) The outside of the case may be loose or cracked
D.) Your computer is getting hotter when you pick it up therefore the fan is like OMG
That is all that I can think of, hope this will shed some light. Sorry for my spelling and grammer.
The best way to find out is to remove the fan and test it. If the unit has no real resistance aside from perhaps the motor it will spin when you blow on it with minimal effort. You can test this without having to take it apart.
But, a friend of mine had this same problem his solution was to beat on the machine until the sound stopped, turned out it was a dislodged wire rubbing against the fan. Resetting the wire fixed the problem. This problem depends on the fan and the model you are talking about.
If you blow across it and nothing happens then most likely the bearing has gone out. Inspect it for dust using a flashlight and be critical, dust will kill a laptop via over heating and breaking a fan is one way it does it.