What is another treatment solution of pus gum aside of root canal and tooth extraction?

Periodontal surgery: If the infection is caused by periodontitis, then periodontal surgery is the answer. If the infection is caused by a non-vital nerve in a tooth, your choices are either root canal therapy or extraction... That's it.

See your DDS: The cause for your condition is not clear from your question. When prescribing a treatment, the etiology for the infection must be known. It would be best for you to attain a proper diagnosis from you dentist and then apply the best treatment for the condition. See your dds.