Setting aside chemical shifts for a moment, I would be inclined to assign my doublet to the benzylic hydrogens (A) being split by the amide hydrogen. And the apparent triplet just might be the hydrogens that are alpha to the thioamide (H).
Now we have to worry about chemical shift. I like to use Hans Reich's site at the University of Wisconsin and also the spectral database of organic compounds. If one compares propionamide with thiopropionamide, the -CH2- group moves downfield from 2.24 ppm in the former to 2.695 in the latter. In other words, your peak at 3.8 ppm has approximately the right shift for the thioamide group. The benzylic hydrogens of benzyl acetamide have a chemical shift of 4.35 ppm, whereas you have a chemical shift of 4.8 ppm and an integral that is larger than the signal at 3.8. One would need a good model, but I find the difference of about .40-.45 ppm surprising (unless the thio substitution also affects the hydrogen atoms adjacent to the nitrogen in the same way it affects the ones adjacent to carbon.
I would say that some of the data agree with your proposed structure, but not all of the data agree.
thiopropionamide: SDBS No.: 5289
benzylacetamide: SDBS No.: 6378