Non-steroidal anti-inflammatory drugs (NSAIDs) are generally utilized for numerous inflammatory ailments. The long-term utilization of NSAIDs prompts adverse reactions such as gastrointestinal ulceration, renal dysfunction and hepatotoxicity; however, selective COX-2 inhibitors prevent these adverse events. Various scientific approaches have been employed to identify safer COX-2 inhibitors, as in any case, a large portion of particular COX-2 inhibitors have been retracted from the market because of severe cardiovascular events. This study aimed to develop and synthesize a novel series of indomethacin analogues with potential anti-inflammatory properties and fewer side effects, wherein carboxylic acid moiety was substituted using DCC/DMAP coupling. This study incorporates the docking of various indomethacin analogues to detect the binding interactions with COX-2 protein (PDB ID: 3NT1). MD simulation was performed to measure the stability and flexibility of ligand–protein interactions at the atomic level, for which the top-scoring ligand–protein complex was selected. These compounds were evaluated in vitro for COX enzymes inhibition. Likewise, selected compounds were screened in vivo for anti-inflammatory potential using the carrageenan-induced rat paw oedema method and their ulcerogenic potential. The acute toxicity of compounds was also predicted using in silico tools. Most of the compounds exhibited the potent inhibition of both COX enzymes; however, 3e and 3c showed the most potent COX-2 inhibition having IC50 0.34 µM and 1.39 µM, respectively. These compounds also demonstrated potent anti-inflammatory potential without ulcerogenic liability. The biological evaluation revealed that the compound substituted with 4-nitrophenyl was most active.