Exercise and injury will always be related, no matter the form of exercise you participate in there is always the possibility of injury. Obviously some activities have a much greater correlation with injury, for example contact sports have a far higher risk of injury compared to walking but so many people still participate in contact sports despite the risks, this is likely due to the physical and psychological rewards it can bring far outweighing the risk of injury.
Listening to your body and seeking the appropriate care is paramount no matter what level of sport or general fitness you are participating in. Obviously different levels of activity will require different frequencies of care and maintenance, for example a professional athlete may see physiotherapists, massage therapists and nutritionists on a weekly basis but your average population will only need to see a physiotherapist when required due to injury or seeing a massage therapist when they feel tight and run down for example.
When it comes to the management of injuries, early detection and action is key. That is why paying close attention to how your body is feeling is so important, if something is not feeling right for a week its more than likely worth getting it looked at. Coaches can be great to go to for mobility advice when you are struggling with things like squat depth, overhead positioning and holding a front rack but they aren't doctors or physios so when you suspect an injury your best bet is to seek professional medical advice. The next step is the most important and often the least adhered to step of injury management, and that is following the rehab plan you are given to treat your injury.
The most common mistake people make is going to a physio receiving treatment on an injury and then returning straight back to what they were doing before, not allowing the body time to heal. Once you have seen a medical professional regarding your injury the best thing you can do is get specifics of exactly what movements you can and can't do, then the next time you are in the gym make your coach aware of these. That way they can do their job of modifying workouts for you so that they can be safely completed. Following injury management plans strictly can prevent acute short term injuries becoming chronic long term damage, sometimes a week of rest as much as it seems like you're missing out and losing fitness can be the best thing for you and is a much better option than continually aggravating an injury leading to months of modified training and the possibility of having to take lengthy time off.