The title, 想ひそめしか (omoi someshika), is of classical origin.
想ひ is an archaic spelling of 想い, ultimately from the verb 想ふ
そめ is the ren'youkei form of the verb 初む・初める ("to begin")
しか is the izenkei form of the particle き・し, which denotes past tense
The original poem goes like this:
恋すてふ わが名はまだき 立ちにけり
"Rumors that I am in love have already surfaced
despite the fact that I was trying to keep my budding love discreet."
Basically it's a poem about the power of rumors lol.
思ひそめしか = I have merely begun to have such feelings/thoughts
or in short, my love is only budding
Then again, I know next to nothing about the context of this song, so maybe my interpretation is severely off. Interpreting it as omoi hisome shika actually makes a clever wordplay, since the original poem was about hidden feelings, too (人知れずこそ) lol