Feeling Tired In Japanese

One of my cognitive stumbling blocks when going from English is to express being tired, which is quoted from Mac OS X Dictionary:

tired |tīrd|
adjective
in need of sleep or rest; wear

In Spanish we have SEUÑO and CONSADO, and in Japanese we have NEMUI and TSUKARETA.

Here's different usages in Japanese:

(1)
運動したから、疲つかれた。
After doing exercise, I am tired.

(2)
薬を飲んだので、眠ねむい。
I took medicine, so I feel tired now.

(3)
花粉のせいで眠い。
The pollens cause me to feel tired.

(4)
昨日、暑くて眠れなかったので、疲れた。
Because last night was so hot, I couldn't sleep, so now I am tired