Badger's eye being pushed out does not sound good, and it sounds painful
If it is a benign tumor it will not spread to other parts of his body but it will continue to grow, so Badger will get worse
Hopefully something can be done
Lilspaz68 may have some ideas or info
Please feed the foods I mentioned above. If badger is unable to eat soft foods (as mentioned in my earlier post) from a dish or off your finger, You can use a one ml syringe (no needle) to feed him the organic soy infant formula thickened with baby cereal - one drop at a time into the side of his mouth so it doesn't go into his lungs. He needs the nutrition and needs to stay hydrated …. dehydration kills. He will need to be fed as much as he wants, every few hours.
Did the vet give you anything for pain?
Keep him warm, fed, getting enough fluids, control his pain, cuddle him, let him stay with his friends, make the cage easy for him to get around in - lower hammocks if he has difficulty with the normal ones etc
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You may need to think about putting Badger to sleep to prevent further sufferring.
Most vet do not know how to do it poperly so you will need to ask questions, and make sure it is done properly. Stay with Badger if at all possible so he will not be frightened ... some vets will allow you to hold him.
The proper way to do it; Badger will be given the gas/oxygen mix used for surgery, when he is unconscious the vet needs to test his eye and toe reflexes (gently pinch his toes) to make sure that Badger is unconscious to at least a surgical level. Once Badger is deeply unconscious, then the vet will inject him. Badger will need to stay unconscious with the gas/oxygen mix until he is dead. Hs breathing will stop and several minutes later his heart will stop beating - I have read that the brain will still be working for awhile. The vet check twice several minutes apart and find no heart beat.
Never let a vet inject a conscious rat into the heart - this is so cruel it is illegal in some places.
I always take my rats home so their friends know what happened to them, and when I have several I pay to have them cremated (I get their ashes back but it is less expensive if you don't)
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I am so very sorry that this is happening to you and to Badger {{hugs}}
Keep Badger as comfortable as possible, and I hope that the vet will have some good news
Hopefully Lilspaz68 will have something hopeful to say
Please let us know what is happening