One major concern is whether there's serial dependence in the differences, due to the observations being over time. The test assumes independence and if that doesn't hold, it could be badly affected. [The rest of my answer is predicated on independence being sufficiently close to true that the null distribution of the test statistic is not badly affected.]
If you want to test the null hypothesis that the pairs of measurements have the same distribution against the alternative that they don't, the Wilcoxon signed rank test will be suitable (there are some other pairs of hypotheses that would fit with the test).
If you want to specifically test for an alternative of a difference in means, the test will be sensitive to that difference (under a null of identical distributions), but the location-shift estimate it gives is not a shift in means (it's the Hodges-Lehmann estimate, the median of pairwise differences; if you like it's the median shift). If your alternative is explicitly a shift alternative, the Hodges-Lehmann estimate will be a reasonable estimator for the population mean of the pairwise shifts.
(In short, if I understand your description, then yes, it looks like a signed rank test would be suitable, but to make your inference about the means you have to make additional assumptions.)
If your interest is particularly in the mean of the differences, I'd suggest looking at a permutation test; with a reasonably efficient implementation, your sample is small enough to cover all possible permutations.