Gotta weigh in here I guess... 21 days seems pretty arbitrary. All things being equal in the small amount you described, I (as a DC, with an MS in rehab and a BS in Athletic Training) would keep all things the same, no increase or decrease in training. How else would you know if the treatment is actually effective? Hell yeah you're gonna feel better if you rest it for 3 weeks! This begs the question, did your doc fix you or did the rest allow you to decrease below your symptom threshold, and will the pain come right back?
In acute cases, yes I tell my patient's to rest/modify activity so the tissue can heal, but chronic (ongoing) pain is a different animal than acute pain in the majority of cases. Not all back pain is the same either, so depending on your pain generator, you could do some back work, and avoid other work. Did he tell you what anatomical structure was the problem or was it the old "Bone out of Place" nonsense?
BTW- What exercises should you not do? Obviously any standing work is out because you have to use your lumbar musculature to brace and stabilize while moving your arms. Sounds like the advice was well intentioned, but just a blanket recommendation, if your chiro knows anything about training, get more answers from him, if not, you may want to look for one that can give you specifics, or you can just be noncompliant with his 21 day recommendation if you want to keep training. Don't mean to undermine your confidence in your doc, but you wouldn't be on an internet forum asking for advice if your confidence was already rock solid...Without having you in front of me, I couldn't say, yes this is ok, no this is bad, I could suggest but by no means give you answers.