The immune system is involved in muscle repair because there is inflammation involved, so there can be similar feelings to being sick. If it feels intense then it means your physical exercise may have been straining and you need to ease into it more. You might have overdone it. Your co-workers are right, your body will adapt, but it will need extra support. The most important thing is to make sure you are eating enough nutritious food to nourish your body, or you will continue to struggle: more protein (like chicken), greens (especially dark leafy greens, broccoli, etc. because they clear out muscle wastes from the body and their nutrients relax muscle tissue), and making sure you are well fed before a big day.
Starting the day with a high protein meal will balance your blood sugar throughout the day so that your body remains fed. Make sure you allow time for genuine rest in your off periods, and if the soreness is fresh and intense use cooling topical creams and even ice if there is a lot of inflammation. Switch to warm (like warm baths, hot water bottles, or heating pads) a couple of days later to help with circulation and repair. Never apply heat to fresh inflammation because it will make it worse.
Last but not least, avoid doing physical work that is above the limit of what you can currently handle. For instance, if you need to lift something very heavy, ask someone to help you. As your body adapts you will be able to do more, but if you continue to overstrain yourself you can develop repetitive strain injury which does not easily go away even if you stop working. "Powering through" is not smart if it's beyond your muscle stress tolerance. Don't be ashamed to ask for help!
The artist's job is not to succumb to despair, but to find an antidote to the emptiness of existence. -W.A.