Recognizing bodily noises (ie, not spoken words) I was pointed here by a chain of stackoverflow posts. I'm a software developer looking to make a module that recognizes noises like snorts and coughs. Here was my original question on stackoverflow and here is where I found this SE board. 

In short, I'm trying to use a Raspberry Pi and a microphone to pick up noises like snorts, coughs, sneezes, etc as a proof of concept to tell if someone is sick. I'm not quite sure where to start, as those posts I linked above have a lot of information. I've also come across this post, but I'm not sure if that helps.

I'm very new here and to this particular concept, so any and all help would be appreciated.
Most likely you are interested in a very simple approach that will run on your Pi. Some of methods I am going to mention are possible to run in real-time with not-badly written C code. Probably you will start with HMM's and MFCC's - it's not a bad idea for the beginning, but as you will see - people developed more advanced methods for such application. Choice of features is rather obvious, pre-processing and Machine Learning is up to you - this will have biggest impact onto your results.
Here is a list of some papers you might find interesting. All of them are targeting cough recognition problem and are applicable to other types of sounds.
HMM-like approach:

Takahashi S., et al. - Cough Detection in Spoken Dialogue System for Home Health Care
Shasha Le, Weiping Hu - Cough sound recognition based on Hilbert marginal spectrum
Matos S., et al. - Detection of cough signals in continuous audio recordings using HMM's
Chunmei Z., et al. - Recognition of cough using features improved by sub-band energy transformation
Hu W., et al. - Cough sound detection bases on EMD analysis and HMM recognition

Karhunen–Loève-like approach:

Liu Y., et al. - A cough sound recognition algorithm based on time-frequency energy distribution

Decision Trees-like approach:

Larson. E, et al. - Accurate and Privacy Preserving Cough Sensing using a Low-Cost Microphone
Martinek J., et al. - Distinction of cough from other sounds produced by daily activities in the upper airways

SVM-like approach:

Jia-Ming L., et al. - Cough signal recognition with Gammatone Cepstral Coefficients

And this is absolutely lovely ;)