Should my aa sponsor be involved in the decision of what anti-depressants I should take?

Probably not. Aa has no opinion on outside issues not related to alcoholism, none, this is why it works. But everybody still has opinions. While any person may have suggestions or personal experience and their insight maybe helpful, the final decision is between you and your doctor. But make sure your doctor knows about your alcoholism.
That isn't your. Sponsor's role. If you wanted to ask for input, that is up to you. The sponsor is there to be of support, not to take over decision making or to take over your treatment plan.