I'm sorry there are so many sad things going on in your life. I especially identify with your tire/spare tire story - which happened to me just a month ago at 11:00 one night.
You sound exhausted! (I wonder why.) :^)
It is a good thing to have a servant attitude - which is different from having a slave attitude. It is good to want to help others. Slaves feel they have to. Servants want to.
It is not such a good thing to serve others so that they will like you. This is not where your value really comes from. I imagine your friends like you for reasons you're unaware of... and doing what everybody calls on you to do is NOT one of them. Your mother was right, but caring people are not the same thing as "people-pleasers." Not by a long shot.
You have a great opportunity now to think about how to do things differently. I suggest that you be too busy for anybody but your family for a little while.
Then start thinking. If you say yes to every little thing somebody asks you to do, you're saying no to a lot of things that might be more important. You may be "sacrificing the important for the urgent," as the saying goes. So save your yesses for the occasions when you know they're absolutely right and necessary. With a little practice you'll recognize those times. But you have to learn to say no first.
You can think about becoming known as the lady who doesn't say yes to everything but who genuinely cares and will help in ways that SHE can manage. At one time I was in a position where going to meetings, etc., was very time-consuming and difficult for me, and I'd say, "I don't do meetings, but call me if there's something I can do to help right here at home." It is also permissible to say, "Not this time - I have as much on my plate right now as I can handle."
You can still care, but put boundaries around it. Aside from a sour word or two from a few (and everybody gets those!), you'll find that you are just as pleasing to others, and perhaps even more genuinely helpful.