This pattern is used when you have a strong emotion, desire, or physical sensation that is almost uncontrollable. It's like saying 'I can't help but feel...' or 'so ... that I can't stand it.' For example, if you're so tired you can't think, you might say 眠たくてしょうがない. It's also used with adjectives to mean 'extremely' or 'unbearably,' like うれしくてしょうがない for being overjoyed.

It's a spoken, emotional expression. You'll hear it in casual conversation and sometimes in writing to convey strong feelings. It's not used in formal business or academic writing. The meaning is similar to 〜てたまらない, but 〜てしょうがない is more colloquial and can be used for both positive and negative feelings, while 〜てたまらない often emphasizes a physical or emotional reaction that is hard to bear.