After running a DRIMSeq pipeline, how do I know which genes are upregulated in the different conditions? After running a DRIMSeq pipeline and obtaining the genes that are differently used between the null and full models, how do I select the genes that are differently used in the different conditions? 

According to the vignette, I would have to use the plotProportions function and say in the group_variable the variable of my interest. What if I want a list of the genes that are differently used specifically in the variables of my interest? Checking every gene manually sounds exhausting. Help would be much appreciated.
After running the test for differential transcript usage you get a list with gene- and transcript-level p-values that you can use to filter which differences are significant. The gene-level p-value tells you if there is differential usage of transcripts within a gene and the transcript-level p-value tells you wich transcripts actually are changing.  Therefor you will want to select significant genes for further investigation. 

The plots are mainly used to visualize top hits as detailed in the vignette.

res &lt;- results(d)
# The data is ordered by p-value
res &lt;- res[order(res$pvalue, decreasing = FALSE), ]
# The top hit is selected
top_gene_id &lt;- res$gene_id[1]
plotProportions(d, gene_id = top_gene_id, group_variable = "group")


However you should consider running the two-stage test that is described on page 16 of the vignette you are using to reduce the number of false positive hits. From this you will get another list of adjusted p-values that can be used as above.