I can find no mention of either firm in the online newspapers (though obviously that is only the ones which are online).
With regard to Harlow & Hinton:
There is no mention of the Firm in the 1884 directory, though there is a Lewis Harlow, working jeweller, at 37 Branston St, and a Thomas Hinton, spoon & fork maker at 48 Northwood St. However Thomas is also listed in 1888 and 1890.
In 1888 the address is Barr St, not Great Barr St
It should be noted that the numbering of Barr St was changed between the 1884 and 1888 directories. In 1884 122½ would have been a part of number 56, which is not listed
1888 Harlow & Hinton , gilt chain makers, 122½ Barr St
1890. Harlow & Hinton have disappeared and 122½ is not listed
Hinton Manufacturing jewellers does not appear in the Birmingham directories for 1932,1933,1936,1937,1938,1939 or 1940, though it may appear in directories outside Birmingham
In passing there is in the 1932 directory, but not in later ones Henry Hinton , metal chain maker, 107½Carver St
Below is a map from the 1880s showing where 122 Barr St was in red. Do not know which was 122a .