I am thinking of cutting my hair short. vs. I am thinking of getting my hair cut short.

Hi there,

Please take a look at these two sentences.

I am thinking of cutting my hair short.
I am thinking of getting my hair cut short.

From what I learned from my english grammar class, the first sentence is not quite right unless you actually cut your hair by yourself.
But i saw in quite a few cases the first expression - not exactly the same, rather of that sort - are used meaning the second sentence.
Is this something that is grammartically incorrect but used often, or just plain wrong?

Thanks in advance... one more... if you found any errors in my writing above, please correct me. It would be greatly appreciated.