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$\ce{CO2}$ reacts with water which is why it enters and exits solution slower than other gasses (if I understand correctly this is why carbonated drinks bubble gradually instead of all at once).
Henry's law is an approximation that assumes the gas solute does not react chemically with the solvent.
Is the Carbonic acid reaction significant enough that Henry's Law does not work for $\ce{CO2}$?
What about in the case of blood, where the reaction is catalyzed by the enzyme Carbonic Anhydrase?
There are multiple forms of Henry's law (see this Wikipedia entry). The net or effective Henry's Law takes into account the other pH-dependent equilibria of $\ce{CO2}$ and carbonate species in water (chemical reactions with water in your question).
In the case of blood, as you said the picture is even more complex. You would have to be careful using, for example, published values of the effective Henry's Law solubility of $\ce{CO2}$ in that case.
