今日は忙しいです。

金曜日なのにやることがたくさんある。
眠たいんですが、「やっぱり」眠るわけがないんです。

Try not to use べき toward yourself, since it is only intended for use in the second- and third- person. Things like this pop up all the time, such as 欲しい and 欲しがる, the first form usable toward first- and second- parties.

You can always consider 眠たくて眠れないんです, but it makes you sound desperate.