Is there special graph paper that can be used to assess the normality of a data set?
Yes there is. It's called "normal probability graph paper"
This is just one example. If you google, you'll find other layouts, that may be more suitable for what you want.
The idea is that you compute the relative cumulative frequency for all values (expressed as a percentage) and plot these on the paper (the horizontal axis representing your values of course).
Then draw a straight line (as well as possible) through your dots.
The better your dots conform to this line, the more 'normal' the distribution of your data set.