Vascular and traumatic injuries of the central nervous system are recognized as global health priorities. A polypharmacology approach that is able to simultaneously target several injury factors by the combination of agents having synergistic effects appears to be promising. Herein, we designed a polymeric delivery system loaded with two drugs, ibuprofen (Ibu) and thyroid hormone triiodothyronine (T3) to in vitro release the suitable amount of the anti-inflammation and the remyelination drug. As a production method, electrospinning technology was used. First, Ibu-loaded micro (diameter circa 0.95–1.20 µm) and nano (diameter circa 0.70 µm) fibers were produced using poly(l-lactide) PLLA and PLGA with different lactide/glycolide ratios (50:50, 75:25, and 85:15) to select the most suitable polymer and fiber diameter. Based on the in vitro release results and in-house knowledge, PLLA nanofibers (mean diameter = 580 ± 120 nm) loaded with both Ibu and T3 were then successfully produced by a co-axial electrospinning technique. The in vitro release studies demonstrated that the final Ibu/T3 PLLA system extended the release of both drugs for 14 days, providing the target sustained release. Finally, studies in cell cultures (RAW macrophages and neural stem cell-derived oligodendrocyte precursor cells—OPCs) demonstrated the anti-inflammatory and promyelinating efficacy of the dual drug-loaded delivery platform.