Is the "GIGABYTE GA-H110M-A" compatible with the "i3 8100" since they have the same "FCLGA1151" socket?
Same Socket: FCLGA1151
or is it only compatible with Z370 motherboards
Not necessarily. You must contact Gigabyte and ask them what processors are compatible with their bios. Then, you can select from those processors.
An upgrade processor must be socket, bios, and chipset compatible.
Also, if compatible, you may need to upgrade the bios BEFORE installing the upgrade processor.