I want to know if it makes sense to run the following analysis on the above data:

1) Paired t-test on each group separately for the group difference in blood sugar means after treatment and before treatment (to test if any increase or decrease in the whole group average is statistically significant) 2) where I start struggling is when I think of the tests to apply for the difference between the groups. I can calculate absolute difference in the means after and before treatment for each group, have then difference of the means after and before in group1, difference of the means after and before in group 2 and same for group 3. Can I run an ANOVA on the difference means between the three groups (mean diff of means after and before group 1 vs mean difference of the means after and before for group 2 vs the one of group 3)?? If yes what other data do I need?