Albert Barnes Commentary 2 Kings 4:23

"And he said, Wherefore wilt thou go to him to-day? it is neither new moon nor sabbath. And she said, It shall be well." — 2 Kings 4:23 (ASV)

Her husband did not connect the illness with his wife’s demand, but thought she wished to attend one of the prophet’s devotional services. It is evident that such services were now held with some regularity on Carmel for the benefit of the faithful in that region.

New moon - By the Law, the first day of each month was to be kept holy. Offerings were appointed for these occasions (Numbers 28:11–15), and they were among the days on which the silver trumpets were to be blown (Numbers 10:10; Psalms 81:3). For this reason, “new moons” are frequently mentioned together with “sabbaths” (Ezekiel 45:17; Hosea 2:11; 1 Chronicles 23:31).

It shall be well - This is better translated as Peace, meaning, “Be quiet; do not trouble me with inquiries, but just let me do as I wish.”