Poison Center Network Enhancement Act of 2018 This bill amends the Public Health Service Act to reauthorize for FY2020-FY2024 and revise the national toll-free phone number, public awareness campaign, and grant program relating to poison control centers. Among other changes, the bill: supports enhancements of the national toll-free phone number, such as texting capabilities and improved location accuracy; expands the public awareness campaign to include education about information that is available from poison control centers regarding drug misuse; and authorizes poison control centers and professional organizations to use grant funds for preventing and treating the misuse of opioids and other drugs.