Am I using these spectra to identify the compound correctly?
Structure elucidation from spectrocopic analysis needs some experience. I have feeling that you are novice to this field by your explanation of the structure. You cannot determine the molecular formula by the data given and, hence you cannot determine the degree of unsaturation of the molecule. Yet, based on $\ce{^1H}$-$\mathrm{NMR}$, you can propose there are at least two aromatic nuclei (probably mono-substituted) in the molecule, be case there is a 10-proton multiplet in the aromatic region ($\pu{7-8 ppm}$). This assignment is supported by the 4 resonances in the region of $\pu{110-160 ppm}$ in $\ce{^{13}C}$-$\mathrm{NMR}$ spectrum. That also suggest these two aromatic nuclei are identical. Two aromatic rings are accounted for 8 degree of unsaturation. 

The given FT-IR spectrum suggest there is a carbonyl group in the molecule, which is confirmed by the resonance at about $\pu{205 ppm}$ in $\ce{^{13}C}$-$\mathrm{NMR}$ spectrum. The peak at about $\pu{205 ppm}$ would also suggest that the carbonyl is not an aldehyde, but a ketone by its chemical shift ($\gt \pu{200 ppm}$), which would be confirmed by the lack of aldehydic peak at about $\pu{10 ppm}$ in $\ce{^1H}$-$\mathrm{NMR}$. The carbonyl group  is also accounted for another 1 degree of unsaturation. 

Now, let's analyze $\ce{^1H}$-$\mathrm{NMR}$ spectrum. There is a 3-proton singlet at around $\pu{2.2 ppm}$ for isolated methyl group (without a neighboring hydrogen), indicating it is a benzylic methyl or next to a carbonyl group. Also, there is another one-proton singlet at about $\pu{5.1 ppm}$ for a methine group (-$\ce{CH}$-), indicating its highly deshielding nature. That deshielding must come from two aromatic ring and carbonyl group together. Thus, based on these data, I can deduct the structure as 1,2-diphenylpropn-2-one as depicted in the diagram below (blue box):


   


The highest peak observed in mass spectrum of the compound at $\pu{210 m/z}$ with law abundance and the base peak ($100\%$ intensity) observed at $\pu{167 m/z}$ confirmed the structure. As depicted in the red box (vide supra), the fragmented cationic radical at $\pu{167 m/z}$ is very stable, which explained the absence of any other fragmentations (as stated by OP, it is the only other significant peak in MS).