しかたがない and しょうがない

A word in the て form plus しかたがない or しょうがない literally means that there is a situation occurring with no way to escape it. These are generally used when the speaker wants to express that they can't control their reaction to something, or that they can't bear it. The latter is more colloquial. It often translates as "can't help X-ing", "can't stop feeling X", or simply "so" (to heighten the feeling being described).

昨日は、4時間しか寝られなかったので、眠くてしようがない。
Yesterday I could only get 4 hours of sleep, so I'm totally exhausted today.

来年、日本に行けることになったので、嬉しくてしょうがない。
It turns out that I can go to Japan next year, so I'm over the moon.

昨日から頭が痛くてしかたがない。メガネが合わないのかもしれない。
My head's been hurting terribly since yesterday. My glasses may not be right.

あの先生の講義は退屈でしょうがない。
That teacher's lectures are so boring.