The red is sunburn did you remove any of the top when's you transplanted. A pruning is in order upon transplant.

Thank you... How do you recommend that I prune it (general advice or a good article that you know of)? I've never pruned a tree before (I'm new at this) and read so many different methods of pruning, so I'm unsure how which method I should use for this new tree. Thank you again. -Jess

The tree still looks pretty good. I would not prune it until late winter. It is dropping fruit because it can not support them or they may have been infected with plum curculio. Make sure and dispose of the fallen fruit, since they can cause a bigger infestation. You may need a second plum tree for pollination if there is not another plum tree close by.

I would not spray with neem oil while in leaf stage since that could cause some leaves to fall off if it is put on too thick. I do not spray anything on my plums except a fungicide to control brown rot and for plum curculio is they are a problem. I do spray a dormant oil and copper in the dormant season.

Agree with Gary, don't do anything except take fruit off for now. Maybe leave one so you can taste the plum this year.

Your one dripper may be going straight down through the potting mix instead of moistening the entire rootball.

In large containers, a mini-sprayer is often more effective.

Stick a finger into various places to determine what is moist, what dry.

Foliar feeding might help. Spray the leaves with dilute fertilizer.