When you have an infection does it affect your absorption of levothyroxine? or is that your body is not functioning properly that makes you feel slugg

Probably both: During illnesses, especially any with stomach or intestinal symptoms, ones absorption of medications with change (but it is not very predictable how much the changes are). With an acute illness, a bigger factor is likely the "malaise" from being ill. As some people say, getting the real flu (influenza) can feel like getting "hit by a truck".