It's a good thing to care and it does make a difference whether you see all the effects on others or not. But if you feel exhausted it may be time to take a look at what is draining you- is it "caring" in general? Probably not. It's probably "caring" about things that you can't influence or change- or you're stuck in a loop on a cause or area that really bugs you and you need a break. So be careful and mindful of who, what, where, and when! It's exhausting to care about things that you can not influence or control - or when you have to pump the breaks because time and patience seem to dictate progress. We all have hot button issues that can affect us to our core or really resonate with us and those are the ones worth caring about. If it's "caring" in general that is exhausting maybe it's time to log off, allow yourself to ignore the news and noise around you, and lean on a new friend or hobby or change in your life that gets you excited about being present. Good luck! And you should be proud to care and feel good about being a mindful, contributing person. Don't envy the ignorant and lazy.
[updated after reading some examples in the comments that OP is giving] Treating others the way you would like to be treated is typically good advice. But if you are using that to nitty gritty your way into empathizing with every little irritation that anybody could have, then you don't get to take care of your own needs sometimes. For your exercise scenario: it's great to be mindful about noise levels for your neighbors- but has anyone ever complained? Would you be particularly bothered if roles were reversed and it was your neighbor working out? What if they gave you a heads up? If it's important to you, don't let an unproven "what if" stop you.