Shame felt over being zoo can come from many different sources.
As for how to get over it, I am sorry, but I am at a loss.
The best thing I could suggest would be reassuring yourself that the common stereotypes of zoophiles do not apply to you. Then, you can sort of "other" yourself from all the hate that zoos get from the public, and remove yourself from any burden that label may place on you.
The public says zoos are abusive and cruel - by treating your companion with respect and dignity, you have removed yourself from this accusation.
The public says zoos only love animals because they cannot find human partners - by realizing that your zoophilia is not a choice and you really do desire animals, you have removed yourself from this accusation.
The public says zoos are at a higher risk of violent crimes - by acting responsibly and not tacking any more negative societal connotations onto yourself, you have removed yourself from this accusation.
The public says zoos are degrading the exalted status of humans by mingling them with lowly animals - well... there really is no solution to this one, it is just dumb on its face
so you can promptly ignore that one. It is fine to admit that!
Repeat this exercise until you do not fit any negative stereotypes of zoos that the public imprints upon you. Afterwards, you can consider yourself to be outside of those that the public is hunting down.
As a word of warning, this will not protect your actual status of safety from the public. Most will not pay attention to the fact that you do not fit their prejudices, and will hunt you anyway if you put the label of "Zoophile" on your head. This is only for your personal mental benefit, as that is the only thing we can control at present.