You won't be able to tell anything with certainty only from the IR, unless you also have the spectra of the desired product.
You should at minimum check with TLC (or HPLC), to see what kind of a mixture you have and if it is worth bothering with the isolation (e.g., doing a
column). The N-alkylated side product could be potentially removed by dissolving the mixture in methyl t-butyl ether and washing it several times with
2M NaOH(aq). This does not necessarily work (some phenols are not extractable into aq. NaOH. Furthermore, it would not remove any of the
N,O-dialkylated product (or any other non-acidic side product).
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