A new computer service will enable physicians in Chicago to supplement a patient's medical history with his history of filing malpractice suits. Physician's Alert is scheduled to begin checking court records, for a fee, next week, company president Michael Eckstein said. The American Medical Assn. reported in January that malpractice suits have increased threefold over the last decade. The report said that there were 16 such claims for every 100 doctors in 1983; fewer than five were filed for every 100 doctors in 1975.