Consider a generalized linear model with the gamma distribution.

Don't worry about the skewed distribution at a single time point. These are samples, and it sounds like the underlying distribution of the dependent variable is approximately normally distributed.

Perhaps this helps: I usually apply the following rule of thumb to address skewness in a distribution of data:

if |skewness statistic|Distribution can be considered symmetrical

Alternatively, I use Shapiro-Wilk to test for normality (symmetric and mesokurtic distribution).