Short answer: Probably.
Long answer: I don't know, what sort of injury do you have?
Of course, each injury is entirely unique - and needs tending to by a medical professional first!! NONE OF THIS ADVICE SUBSTITUTES SEEING YOUR DOCTOR OR PHYSIO.
But here are some general rules of thumb for wanting to keep some element of fitness and strength going if you are working with an injury:
1. Don't move into pain. Pain is your body saying stop. Listen to it. Don't just finish the set or the run or keep doing it because you just love doing it. Play the longer game and see the bigger picture. If you try and push through pain, you'll likely damage yourself more and put yourself out of action for longer.
Avoid pain in everyday activities where you can also, not just in exercise.
2. Is it a shallow, acute pain? That eases fairly quickly, and in 1-2 weeks is a-ok? It's likely to be muscular and should be rested. Is it a deeper, duller pain? It's probably not muscles and it could be tendons or ligaments. Tread carefully. They take a longer to heal (more like 2-6 months, even longer sometimes), as they have a poorer blood supply. Get an expert opinion.
3. In some instances - can it be worked around? For example, I once had a client who injured her shoulder in a fall. Physio assessment wasn't an option (first lockdown!), so we experimented with push variations that didn't hurt (we found keeping the elbows in to be a winning position), did a ton of rotator cuff exercises - and happenstance it worked (the plan was still to see a physio when she could). But after 6 months, her shoulder pain was gone - and she'd achieved her first full push up!
Another example is if the injury is just on one side of the body. It is VERY USEFUL to keep training the non-injured side e.g. if you've broken your arm or your leg, then work the other ok arm or leg. Why? Because you are continuing to train your nervous system and the some of the gains made do transfer to that side of your body not working.
If the injury is in your upper body - do you still have a pair of legs? Train those.
If the injury is in your leg - do you still have arms? Train those.
Get creative. Do the thing.
4. Heat and cold probably do both help. If it's an acute injury (short term painful), then alternate icing and heating may help, as may taking pain-relief and/or anti-inflammatory medicine, along with rest and raising up the injury. None of these are long term solutions; if they don't work after 2-3 days, don't keep dosing up on pain relief. Go get checked out.
Remember - the price of being an active person is probably injury at some point. The price of being a non-active person is definitely injury at some point. You didn't necessarily do something wrong to get injured. Or, you know, maybe jumping off that bench into the paddling pool wasn't in fact the best idea.
Remember also; most injuries don't last forever. I have worked with frozen shoulders, hip impingements, shoulder pain, torn quads/hamstrings/calves, pelvis pain, knee pain.... and they usually do not last forever. Keep seeking help, get advice, follow the advice and trust that your body will heal. It's pretty good at the recovery malarkey when we give it a chance.
What has been your biggest injury frustration? What is the worst injury you've had that you've come back from?
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