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The fact that this has lasted two weeks, means it is either low grade bacterial or fungal. Viral illnesses have a life cycle that tend to be shorter, unless they are secondarily infected by a fungus or a bacteria.
So you will invariably need a broad spectrum antiseptic mouth wash/gaggle, if you insist on OTC treatment. (My instinct is that a prescription grade antibiotic /antifungal either orally or as a gaggle will work faster/more effectively as per cost:benefit ratio)
The OTC meds will be combining nystatin drops twice daily after chlorhexidine solutions gaggles.
Prescription grade would have been Amoxycillin (safe for breastfeed) and caps fluconazole