GPs are there to help, not report and you can't expect your husband to sympathise and understand if he doesn't know what's going on- I have been where you are and it is hard, I do think a psychologist could be agreat help but unless the GP knows what is happening they won't do a referral for you. I agree that re-homing some of the animals is a really good idea- much better than having too much on your plate when the baby arrives.
See if you can find time for a few Yoga breathing exercises, they feel odd and sometimes silly at first but they can really help especially if you are prone to panic attacks and hyperventilation ( I was) humming bee breath and yoga nidra are good places to start and you don't have to tie yourself up in knots! Google them!