Listed in Gary W. Webster's "Confederate Roll of Honor: Known Confederate Dead, Vicksburg Campaign, January 1862-July 1863" ("Ole Sow" Publications, 100 Walnut Circle, Vicksburg, Mississippi 39180):

>>> Whittemore, H. S., Lieutenant, Company I, 28th Louisiana, died 31 MAR 1863, UDC Record page 27, body sent home. <<<

According to Dr. Bergeron's "Guide to Louisiana Confederate Military Units, 1861-1865" (LSU Press, 1989), the regiment is Allen Thomas' 28th/29th Louisiana Infantry and Company I was the Calcasieu Tigers from Calcasieu Parish. A good closure to this discussion would be to find his final resting place