Hi ampws,

If I understood correctly, you have a single variable measured for 120 individuals, separated in two groups. You then tested whether there was difference in those two groups. Now, for only 20 individuals you added a drug and measured again and want to test for differences between the initial state and the "after". I wouldn't rely on parametric tests that are based on normality assumptions for this case, first because of the sample size and also because of the non-normality found in the whole dataset. A safer approach would demand some non-parametric test for paired data, equivalent to a paired t-test, such as Wilcoxon's signed rank test. I'd recommend that over parametric tests, even if the subsample is approximately normally distributed.

Good luck