Antibiotics are often misused, especially for the treatment of upper respiratory tract infections (URTIs) in children, where their use is unnecessary and leads to antimicrobial resistance. This study sought to explore the knowledge, attitudes and practices (KAP) of parents and pediatricians on the use of antibiotics among children and whether the level of education of parents has an impact on their KAP. The research was carried out among 1459 parents of children under 6 years of age and among 18 pediatricians. Sixty percent of pediatricians (61.1%) were prescribed antibiotics daily in their practice. Most of the surveyed parents (98.4%) state that doctors are their main source of information when deciding on the use of antibiotics in the treatment of their children. Parents with a higher level of education use television less often as a source of information when making this decision compared to parents with a lower level of education (p = 0.039, i.e., p = 0.003). The majority of parents (80.7%) knew that Panklav (amoxicillin/clavulanic acid) is an antibiotic, while 52.5% identified Pancef (cefixime) as an antibiotic. Parents with a higher level of education correctly identified antibiotics significantly more often (p < 0.001). This study shows that in the Republic of Srpska, parents have adequate knowledge about antibiotics, especially those with a higher level of education, who show better KAP when it comes to antibiotic use.