In many cases, you can use a t-test to compare means of non-normally distributed data sets, as the mean of a large number of non-normally distributed data is approximately normally distributed:
Why is a sum of skewed left distribution normal distributed according to the central limit theorem
If you do not want to go that route, you would need to make assumptions about the distribution of the data in the other studies. Just because they publish mean and CI does not mean, they found normally distributed values. If, for example, there was reason to assume, those other data were poisson-distributed or any other reasonable assumption, you could simulate a lot of datasets from suitable distributions and compare that with your data. Do you have any helpfull knowledge in that respect?