Missing my pets at uni :(Watch
Also, I think your problem is more to do with your mental health and less to do with your pets! Your pets are a source of comfort and regularity in your life, and you want that back since you are in a foreign environment.
Is there any way you could find a 'comfort object' to hold when you miss your pets? For example a stuffed animal or something. I know it's a bit childish but in psychology a lot of people benefit from finding a comfort object when they have poor mental health.
You also need to get to the root of what is causing mental health problems. Have you considered going to therapy to figure it out? To be fair, everyone feels lonely and a bit depressed when they go to uni for the first time, missing home and everything. I know for a fact that you will settle in and learn to love it. And maybe if you're really struggling you can take a train to go back home and see your pets one weekend? It's hard for you at the moment so you should allow yourself to do so if matters get really bad.