This is most likely inflammation and commonly ocurrs with Hydroquinone or Retin-A whichare common ingredients in "bleaching" formulas.
Oftentimes these medications are combined with steroid creams to lessen the effect of the irratation. Some of these are formulated in triple preparations. One of these is called Triluma.
Typically over-the-counter steroid creams are not strong enough to counter the effects.
The redness should be treated or you could possibly develop post-inflammatory hyperpigmentation. This should be prescribed and monitored by your practitioner.
Also, you may want to consider cessation of the product but please consult with your cosmetic provider.

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