Friend, I am sorry your cat is not feeling well. In response to your question, when a cat is walking like if he is drunk this can be caused by many different medical conditions. In general, we can classify this in two main categories:
1- Central nervous system disorders. Ex: Vestibular disease, infections, thromboembolic (stroke like), etc.
2- Systemic diseases: Diabetes, heart disease, urinary blockage, toxicity, liver disease, anemia, fever, etc.
The fact that he is so lethargic and you are seeing pale gums I would want to rule out a systemic disease. Unfortunately, we are very limited as to what you can do at home. I am a bit concern about his current state, this could be fatal if he not treated by a veterinarian quickly. There is really nothing that I can recommend for you to do at home that would have a significant therapeutic benefit, I am sorry. I would strongly recommend taking him to the nearest ER veterinarian. I realize that this answer may not be entirely to your liking, and I regret being the bearer of information that you really don’t want to hear. But it would be unfair to you and unprofessional of me were I to provide you with anything less than truthful and honest information. I hope you understand.
In response to your question, yes, if he is blocked you could easily feel a distended large bladder in the mid-caudal abdomen.
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