Parametric or non-parametric for 2 sets of data being compared one normal one not

Hi folks, I am in a dilemma and maybe one of you can help. I have 2 sets of data, one from a control group and one from an experiment group. Each group took a test before and after a period of time and difference calculated. When checking for normality within the data via Anderson-Darling I find that the control group has a P-value of >0.05 so the data doesn't significantly deviate from a normal distribution. However my control group has a P-value of less than 0.05 and so does NOT follow normal distribution, the problem I have is I want to compare the 2 sets of data and show that the experiment group changed(improved) due to an intervention. Do I need to use both parametric (paired t-test for the normally distributed set) and NON-parametric (Mann-Whitney) for the experiment group (not normal dist.) Can I do this or do I use non-parametric on both since they are to be compared with each other.

Help will be appreciated. I'm confusing myself.