I would assume it if was in the common areas and not an obviously personal item (ie toiletries or clothing) that it would be ok for me to use.
If you want to keep that particular blanket for youself, i would consider keeping one out for her to use, and telling her that you prefer that one, so you've brought her one out to use.
You're in a difficult situation. As a lodger, you need to decide what is reasonable for her to use without asking, and what isn't, and maybe give her some guidelines. I wouldn't have anticipated a problem if I was her.
I would assume that the blanket was available for anyone who was allowed to use the living room.
But you know what? It doesn't matter. Just say, "You know, I'm sort of attached to that blanket, it's special to me, and I don't want to share it. If you'd like to have a blanket here in the living room, you should bring one of your own out and leave it here. Also, please be sure your guests don't use it. If you're having company, help me remember to put it in my room, okay?"
I might also have assumed that the OK for headache tablets meant other days too, but then I would *also* assume that meant I needed to buy the next batch when they were getting low. (At the very least, I'd need to alert you, but I'd also think I needed to pitch in monetarily.) I might think they were "household" stuff now, but I'd think I needed to buy it.
Did you ever say anything about the headache tablets? You are allowed to, even now, and you should have then. You don't need to get mad about it--just be matter-of-fact. Assume that she's a reasonable person and just spaced out. So say: "I saw that you had used up the headache tablets. If you're going to use them, you need to replace them when they run out. They're not covered in your rent, and you'll need to replace what you use up."
or say, "I saw that you had used up the headache tablets. I was willing to give you one in a pinch, since you didn't have your own that first night. But I expected you to purchase your own supply the next day. I do not want to share medications and other things like that. So please buy your own bottle, and then let me take a few to replace the ones you used up."
Speak up! Speak up before you get really mad. (OK, maybe you're miffed right away--I would be, probably.)
Be straightforward. To help you keep from being unpleasant/attacking/whatever in your tone of voice (and making things worse), try to get into the mindset that you're informing her, not scolding her.
It might help to remember that yes, some of us do think that the assumptions wasn't THAT far off. So she's not that horribly "entitled," but you *do* want to establish boundaries. You're entitled to.
But you should ALSO be direct. No hinting. Say, "I don't want other people to use my special blanket." Then you can also say, "here's one you can use for the time you're living here," or you can say, "You'll need to get your own."
But a boundary is *clearly drawn*. It is not hinted at. "Good fences make good neighbors," and a good fence is VERY VISIBLE. It's not hinted it. It's right there, crisp and clear. It's not nasty or mean, either. It's just there.