In the context of the globally growing problem of resistance to most used antibacterial agents, essential oils offer promising solutions against multidrug-resistant (MDR) bacterial pathogens. The present study aimed to evaluate the prevalence, etiology, and antibiotic-resistance profiles of bacteria responsible for pyogenic infections in Regional Military University Hospital of Constantine. Disc diffusion and broth microdilution (MIC) methods were used to evaluate the antimicrobial activity of essential oils from five Algerian aromatic plants growing wild in the north of Algeria—Salvia officinalis (Sage), Thymus vulgaris (Thyme), Mentha pulegium L. (Mentha), Rosmarinus officinalis (Rosemary), and Pelargonium roseum (Geranium)—against reference and MDR strains. During three months of the prospective study, 112 isolates out of 431 pus samples were identified. Staphylococcus aureus was the most predominant species (25%), followed by Klebsiella pneumoniae (21.42%), Pseudomonas aeruginosa (21%), and Escherichia coli (17.95%). Among pus isolates, 65 were MDR (58.03%). The radial streak-line assay showed that R. officinalis and M. pulegium L. had weak activity against the tested strains, whereas P. roseum showed no activity at all. Meanwhile, T. vulgaris was the most potent, with an inhibition zone of 12–26 mm and an MIC value ranging between 0.25 and 1.25%, followed by S. officinalis with an inhibition zone of 8–12 mm and an MIC value ranging between 0.62 and 2.5%. Generally, A. baumannii and S. aureus ATCC6538P were the most sensitive strains, whereas P. aeruginosa ATCC27853 was the most resistant strain to the oils. Gas chromatography–mass spectrometry analysis of chemical composition revealed the presence of borneol (76.42%) and thymol (17.69%) as predominant in thyme, whereas camphor (36.92%) and α- thujone (34.91%) were the major volatiles in sage. The in-silico study revealed that sesquiterpenes and thymol had the highest binding free energies against the vital enzymes involved in biosynthesis and repair of cell walls, proteins, and nucleic acids compared to monoterpenes. The results demonstrated that T. vulgaris and S. officinalis are ideal candidates for developing future potentially active remedies against MDR strains.