There is no primary evidence to suggest that Gallienus was gay, though it is not beyond the realm of possibility. If he was gay, he wouldn't have been the first homosexual Emperor. Hadrian was known to have had a passionate relationship with a young man named Antinous. The fact that Hadrian had his beloved deified after his untimely death is a testament to the intensity of their relationship. In any case, there is no evidence that suggests Gallienus was gay and the fact that he had several children makes it more than likely that he wasn't. To say otherwise is pure speculation.

In regards to Gallienus possibly being a trans-woman, again there is no evidence that suggests this and, again, to suggest otherwise is pure speculation and wild speculation at that. While homosexuality was accepted within Roman society, crossdressing, for want of a better word, was most certainly not.

As noted by u/ReasonedRedoubt, Emperor Elagabalus would certainly be a better fit for the character you have described.