Good Morning and welcome. I am Dr. Loretta, a licensed veterinarian and I am happy to answer your question.
I fear that this swollen lip is caused by an Eosinophilic complex that affects cats. This can be very painful and only responds to steroid injections. Check to see if your vet has given this medication.
This condition is causes granulomas and ulcers that are extremely painful and responds to this medicaton. This cannot be cured but can be maintained.
This also could be due to an abscess that has formed in this area and this will require antiibiotics...your vet needs to determine what this is and then treat accordingly. This also could be a tumor, either benign or cancerous and a biopsy will tell if this is the case.
This LINK will explain in more detail.
Does that make sense to you?
Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please Reply so I can clarify for you
Sincerely, Dr. Loretta