mourning vs sorrowing

mourning is a noun but sorrowing is not a noun.

Word	Noun	Adjective	Verb	Adverb
mourning	Yes	Yes	No	No
sorrowing	No	Yes	No	No

As adjectives, mourning and sorrowing are synonyms defined as:

Other synonyms of mourning include bereaved, bereft, grief-stricken, grieving.

mourning (noun)	sorrowing (noun)
the passionate and demonstrative activity of expressing grief
state of sorrow over the death or departure of a loved one

mourning (adjective)	sorrowing (adjective)
sorrowful through loss or deprivation	sorrowful through loss or deprivation