No, you should not.  Doing so inflates the probability of a Type I error.  In most reviews you'd get skewered for this practice.  

Contrasts is a move to the right direction with these tests, but what is the "right" interpretation of the p-values depends on how many tests the contrasts perform. For example, pairwise comparisons in ANOVA designs are a form of contrasts. If you manage to make a single contrast that produces one p-value, then you don't have a multiple testing problem. Here the question is in locating differences among group and time pairs, so a single contrast is not likely to produce the answer @Hanot is looking for. However, with more than one test the chances of obtaining spurious results increase. A simple but brutal correction often used is the Bonferroni correction, where you alternatively call the contrast result significant if it falls below the significance level (e.g. 0.05) divided by the number of tests.

In this case it would be ideal to construct contrasts testing the interaction within each group and time point pair. For example, the contrast cont1 = T1(before)-T1(right after) - T2 (before) + T2(right after) gives a raw p-value for the interaction between groups T1 and T2 between the two first time points. Proceeding in this way you can see that there are three interaction tests for each pairwise group comparison over two time-points (T1 vs T2 in time-point pairs: before - after, before - after 30 min, after - after 30 min). If you are looking at all group pairs, then there are six different group pairs, which multiplied by three gives the total number of contrasts as 18. Now with Bonferroni correction, you would call an interaction contrast significant within 18 independent tests if the p-value was lower than 0.05/18, which is approximately = 0.0027778.

If you initially planned the study exactly these contrasts, then you would be permitted to look at the corrected p-values from the contrasts. This is something that is generally feasible in randomized trials, because the intent has to be formally submitted to some registry prior to collecting data. For instance, to increase power you could restrict the number of tests in the planning of the study to just the consecutive time point pairs (i.e. before - after 30 min would not be tested) OR you could simply test if there was a group pair difference anywhere in the time-dimension (in this case you would not be able to say where in time the difference was significant) OR you could use some other contrasts depending on what your research question calls for. However, if your data is collected in the observational design (non-experimental), there probably was no a priori comparison in mind and then you would be stuck with the 18 comparisons. There are other (less stringent)ways to do the p-value correction (see e.g. p.adjust-command in the free R programming environment).

A good reference for multiple testing is: Moyé LA. 2003. Multiple analyses in clinical trials: fundamentals for investigators. New York: Springer.

In relation to the original question: the corrected pairwise results will probably mostly not remain significant after the p-value-correction. In any case, you could report the adjusted p-values for the contrast comparisons, if you can make a case that they were planned a priori. Otherwise it may be reasonable to rely on the multivariate test rather than the one-way tests. It is difficult, however, to give precise advice with a limited information about your study.

Can you try hierarchical (nested) design using excel or R program

https://plantmethods.biomedcentral.com/articles/10.1186/s13007-015-0091-5

I agree with both Michael E Young and Timo Törmäkangas . They both say yes but you have to do it correctly. best, David Booth