To determine the safety and usefulness of zidovudine (AZT) for the treatment of children 3 months to 12 years of age. This study is designed to determine if children who are infected with HIV and who have a special type of lung disease called lymphocytic interstitial pneumonitis (LIP) or other early symptoms of HIV infection may derive benefit from treatment with AZT. It is hoped that this drug will prevent children from developing additional symptoms and infections and will help resolve already existing symptoms.