てしょうがない: an intensely felt state one cannot control
Learn てしょうがない for the strength of an emotion or sensation. Separate standalone しょうがない expressing resignation, preceding negative content, and actual resulting actions.
Intensity of feelings and sensations
試験の結果が気になってしょうがありません。 means that the exam result is intensely on the speaker's mind. It expresses concern about the result, not confirmation that it has been checked.
今日は眠くてしょうがないです。 describes being extremely sleepy today. I-adjectives connect with くて; na-adjectives take で, as in 心配でしょうがない.
Positive feelings and negative content
久しぶりの旅行が楽しみでしょうがありません。 expresses intense excitement about a trip after a long interval. Anticipation alone does not tell us that the trip has already been taken.
気に入らなくてしょうがない means disliking something intensely. The preceding negative content is intensified, not combined with the final ない to reverse it into liking something.
Comparison with standalone resignation
もう終わったことだから、しょうがありません。 expresses resignation that nothing can be done about something already over. Unlike the intensity in 眠くてしょうがない, it evaluates the situation as lacking a remedy.
足が痛くてしょうがなかったので、休みました。 reports that the speaker's feet hurt intensely, so they rested. Preserve both the pain and actual rest rather than changing the latter into a wish such as 休みたい.
Quick check: Does 会いたくてしょうがありません。 mean no longer wanting to meet someone?
Show the answer and why
No. It expresses an intense wish to meet. 会いたい is strengthened; do not interpret しょうがない as an isolated negative.