If by "my sometimes-worried emotional state" you mean "my emotional state that is (or was) sometimes worried", I think a hyphen is optional in this context.
"Sometimes" is an adverb. There is a common rule that forbids the use of a hyphen after very or after an adverb formed with -ly. But sometimes isn't in either of those categories. The Handbook of Good English, by Edward Johnson, recommends using a hyphen after adverbs that have the same form as adjectives when the are part of a phrase that precedes a noun (e.g., like half or well in phrases like "a half-eaten apple" or "a well-known book"), but "sometimes" is rarely used as an adjective, so I don't think it would really fall into that category either.
I looked through the Google Books results for "sometimes difficult task" (the presence or absence of a hyphen is ignored) and found many examples of the spaced spelling being used in published texts, but only one example so far of the hyphenated spelling being used:
In the mean time, we hope this book helps both amateurs and professionals with the sometimes-difficult task of positively identifying species of marine mammals they see alive or encounter dead.
(Marine Mammals of the World: A Comprehensive Guide to Their Identification, by Thomas A. Jefferson, Marc A. Webber, and Robert L. Pitman. Academic Press (Elsevier), 2008. p. 1)
Interestingly, this seems to have been intentionally added at some point, as a 1993 version of the document uses spacing with no hyphen (Rome, FAO).
If you mean "my emotional state of 'somewhat worried'", there might be a stronger argument for using a hyphen, since in that case "somewhat-worried" might be taken as a kind of makeshift compound. But I'm not sure how likely that interpretation of the syntax is. While thinking about this question, I started to feel that it sounds a little odd to me to use an emotional-state adjective before the word "emotional state" (e.g. I wondered "is it really the state that is worried, or the person?"), but I think my feeling (which isn't very strong to begin with) is probably not based on a valid judgement, since I see many Google results for things like "angry emotional state" or "sad emotional state".
Anyway, I think I would not use a hyphen.