Using both 'concurrently' and 'also' is a bit redundant. I would remove one or the other. I would use one of these:
I was also dreading the return home, though. Concurrently, though, I was dreading the return home. Concurrently, I was dreading the return home, though.
'concurrently' might be in a higher register than you need. You can use 'at the same time' instead.
Thank you for the clarification and for the hint about also. The higher register isn't a problem. It is what I am aiming for in my novel. It is a literary attempt to dazzle the mind. Or it might just fail miserably.