Just started a new, physically demanding job. Reddit, please help me adjust my weight training around it?

I've just started a new job which I love! I work for a charity and collect donated furniture/deliver purchased furniture. It's a lot of heavy lifting and after my first week every single muscle seems to have gotten a work out and is sore and taut, which is great.

The thing is, for the last 6 months I've been going to the gym 5 days per week to work on one or two individual muscles per day in order to build myself up, particularly my arms and chest.

I read a lot about the importance of letting a heavily worked on muscle rest and repair afterwards so my worry is this- If I go to the gym in the morning and train, say, my arms and chest and then go to work for 8 hours of general lifting and exercise, will the fact that those muscles don't get their rest period affect their growth? Should I do my weight training in the mornings before work of afterwards? Obviously the gym session works the muscles harder but they aren't going to get a break until I get home. Fortunately the job affords the opportunity to eat as often as I like so I can take several packed lunches with the right nutritional content and give my body what it needs.

What would be the most beneficial way to train around this job for muscle building?