"Tonight is the first night that I'm actually feeling the fatigue of...X" - that is much more preferable in this sentence than where.
I think you can say "feeling the fatigue" if you qualify it. For example, "Tonight is the first night that I'm actually feeling the fatigue that comes with the summer heat."
I'd suggest you to use niether of the two words in this context. When we talk about time, we often use 'when', and for places 'where'. Also, 'fatigue' as a noun itself means 'a feeling of being extremely tired'. So saying 'feeling the fatigue' makes the sentence verbose. You can say:
Tonight is the first night when i'm actualy feeling fatigued(here