While your birds injuries may not have been immediately life threatening, there may be broken skull bones, fluid in airways or other injuries that need attention by a professional. Further, flesh wounds will rapidly become infected due to oral bacteria from bobcat, feathers and debris pushed into wound and exposure to outside. Your goose at least needs examination and antibiotic treatment. see a veterinarian immediately to prevent a worsening, and likely life threatening result.
Dr G
Thank you for your help! Our usual vet was closed last night and the only other one that was open refused to see him unless we paid them upfront. (They were going to charge us an extra $100 for an "afterhour fee" and we were between paychecks... He survived the night and the gargling/snoring sound has stopped but now there's a slight whistling sound that appears to be coming from his nose. We took him to my aunt who is a nurse and she bandaged him up and stopped the bleeding. (She was our only option at the time) We made plans to see a vet today but the avian specialist we spoke with on the phone said that we should wait a couple days to see if he has any more improvements. I guess he was trying to save us money because he said that they really can't close up the wounds, for risk of infection. We will continue to monitor him and take the appropriate actions needed.
Thank you again for the advice and taking the time to reply! :)