Makes much more sense now 
But if the (n+1) rule is based on number of Hydrogens on neighbouring carbons, why does the lone H in the carboxylic acid produce a singlet? It is not a carbon atom and has no carbon atoms attached to it?
It produces a singlet because it doesn't have any neighbouring carbon atoms w/ hydrogens bonded to it. Remember, it's the n+1 rule, so no neighbours (n=0) becomes 0+1 a.k.a a singlet. If you've got no neighbours, you're a singlet, if you've got two neighbouring hydrogens, you'll have triplet etc.
The lone hydrogen will be picked up on the HNMR because it's own hydrogen environment. The signal produced doesn't depend on the carbons, just the different hydrogen environments. It's the
splitting of the peaks which are determined by the neighbouring hydrogens on the carbons.
I really hope this makes sense! I'm not the best at clear explanations!
When you use the (n+1) rule, don't you look at a specific carbon atom, then the number of hydrogens on neighbouring/adjacent carbon atoms?
Why then does the lone H produce a singlet, if you are supposed to look at a carbon atom instead when using the (n+1) rule? Thanks 
You use the carbon atom, yes, to identify possible neighbours for peak splitting; however, that's it. The fact that the hydrogen is bonded to an oxygen rather than a carbon does not mean it won't produce a peak. It's still a different hydrogen environment. It's the fact that it has no neighbouring carbons which leads to it just being a singlet.