No thanks, I'm specifically asking for an explanation of how it affects me.
What your cells feel, are signals from your immune system (cops) to "freeze and stop doing shit". This message is delivered in the form of cytokines. What happens inside the cell, is metabolism slows, and recycling begins. Too much of this leads to atrophy.
At the organ level, this causes various diseases of aging. Muscle wasting. Brain atrophy. Liver disease (alcoholic or dietary).
More seriously, your question, as stated, can only be answered by your doctor and then probably only after taking various samples. What is worse is that inflammation is typically a response to something else, so it is at least a second order symptom rather than a primary cause. (for example your sore throat is from inflammation, but the inflammation is from a response to something the mucus membrane didn't like. Could be a cold, it could be the chlorine you drank.)
Symptoms associated with inflammation are aches, pain, vomiting, diarrhea, fainting, swelling, and itching at least. If you have any of those symptoms, it is affecting you.
A sore throat, is caused by inflammation of the mucus tissues in your throat, for example. A mosquito bite itches due to inflammation, it is the immune response to the mosquito's saliva that you feel as an itching sensation.
The 'new' thing however is that this mechanism can occur pretty much in every cell of your body and some people have speculated it is the root of a number of ailments. Google 'inflammation' on scholar.google.com and you will find a number of papers discussing different ways that it can affect you.