My teacher gave me this definition for phenotype:

'Your outward physical appearance for a SPECIFIC characteristic.'

I looked this upnon the internet afterwards and it said something like:

'Your observable appearance of ALL your characteristics' (something along those lines)

So anyway, is my teacher's definition a good one? If not can you provide a better one please. Thanks.

It can be either, really, depending on what you are interested in.  If you are looking at the genetic and/or environmental basis for a particular trait, then your phenotype is what you can observe about that specific trait. 
However, your phenotype in general is everything observable.

I would like to note that this includes behavior (what you do), not just how you look.

I agree with Ajna but it is a term used slightly differently in different areas of biology. I have certainly come across biologists who us "phenotype" to mean morphology only but this is - in my view - quite wrong! Increasingly people are referring to the whole multivariate phenotype (i.e. including all traits you can think of and measure/observe) as the phenome.

As an aside...this means that studying phenotypes can be called phenomics which  - if I was a cynic - I might think was simply a way to join the club of new names for biological subjects. We've had genomics, post-genomics, transcriptomics, proteomics, metabalomics, and now phenomics.... I'm hoping ecology will be rebranded as eco-nomics next - just to cause confusion!