Sodium + water reaction, noxious fumes? I was reacting pure sodium and tap water, and at one point I put some splattered sodium back into the water. I observed fumes that reacted with my respiratory system, producing a burning sensation.

I read that it is possible to produce sodium oxide fumes from sodium hydroxide at high temperatures (the sodium did burn at the end, producing an orange flame).

My question is what could be the chemical composition of these fumes?
I agree.  This is a dangerous reaction and should not be tried without proper equipment, including a lab hood and fire extinguishing equipment.

The fumes could be "just" droplets of sodium hydroxide solution.  I've seen similar fumes involving hydrochloric acid, just by adding water to rinse out traces of concentrated acid (in a hood, of course).  They may be carried by increased evaporation even without boiling and without need for a further "chemical reaction".