We demonstrate that the thermopower (S) can be used to probe the spin fluctuations (SFs) in proximity to the quantum critical point (QCP) in Fe-based superconductors. The sensitivity of S to the entropy of charge carriers allows us to observe an increase of S/T in Ba(Fe1-x Co-x)(2)As-2 close to the spin-density-wave (SDW) QCP. This behavior is due to the coupling of low-energy conduction electrons to two-dimensional SFs, similar to heavy-fermion systems. The low-temperature enhancement of S/T in the Co substitution range 0.02 < x < 0.1 is bordered by two Lifshitz transitions, and it corresponds to the superconducting region, where a similarity between the electron and nonreconstructed hole pockets exists. The maximal S/T is observed in proximity to the commensurate-to-incommensurate SDW transition, for critical x(c) approximate to 0.05, close to the highest superconducting T-c. This analysis indicates that low-T thermopower is influenced by critical spin fluctuations which are important for the superconducting mechanism.