I feel like my mood is slightly elevated when I'm mildly sick (or physically worn out). It's like I reach a state of contentment and also get bored less easily and more motivated to do things I normally hate doing. Does anyone else experience this too, or am I the only one?

Yap, such things happen. Interesting feeling indeed.

Maybe the immune systems starts to work and the very small bugs leaving on you (I mean some bacteria) are getting much more absorbed with other activities, so your consciousness gets freedom of actions? In Anyway the dynamic of some processes changes and the mood changes. Interesting phenomena indeed.