Thanks guys. Fixbutte - interesting to know that Latricia Walker was Phyllis Otis. I can add too that Gladyces (with an acute accent over the "e") Carter De Jesus was born in 1911 and was copyrighting songs as early as 1945. Copyrights were still being filed in her name as late as the 1980s. She was affiliated with at least 15 publishing imprints and there were also songs filed by her with various collaborators without benefit of publishers. Keith, she had several songs in the late fifties filed by Chico (or Chico's) Music Co and at least one of them found it's way to Juggy Murray at Sue. And interestingly I have 1958 and 1968 listings that place Chico's Music Co. at 309 West 100th Street, NYC, c/o Gladyces De Jesus! In 1957 (and perhaps earlier) Chico's was at 156 West 42nd Street.
Gladyces DeJesus again, as you have also wondered, mickey rat:
One credit in the Catalog of Copyright Entries: Third series says Gladyces Carter DeJesus, and there is an article from 1975 on the web titled The Death of Boogie Woogie: A Ritualized Scat-Song in Thirteen Beats by Paul Carter Harrison that is "Dedicated to composer-lyricist Gladycé DeJesus", so I guess that these two were related and, apparently, Gladyces (Gladycé) DeJesus was a real person.
There is an apparent connection as well between Johnny Otis and the record's other composer, Gladyces DeJesus, who is credited not only on all four Henry Hill records but also on at least two Little Esther recordings, "Don't Make A Fool Out Of Me" and "I'm A Bad Bad Girl". Unfortunately, there is nothing to find about this person but composer credits.
Images for this one and another one (Federal 12037) by Henry Hill added. All of your copyright information complies with these labels, except for "If You Love Me" which is also the A-side ("AA") here, not the B-side. On further research, however, it seems obvious that the composer credit given on the label, Latricia Walker, is the birth name of Johnny Otis' wife Phyllis Latricia Otis, who died on September 25, 2016 at the age of 94, four years after her husband with whom she was married for 71(!) years, see Phyllis Latricia Otis obituary. So quite probably Johnny Otis, who is not mentioned anywhere on the record labels, used his wife's name as a pseudonym for contractual reasons.