You can act or look like a slut in as much as your manner of dress, makeup, and behaviour suggests that you are on the lookout for a man, any man, because you want or need the confirmation that you are sexually attractive. In this case, a slut (technically speaking) is not, and never is a prostitute, but a promiscuous woman or one who at the very least gives that impression.
If a woman is slutty or sluttish, it could mean her appearance is slovenly, her makeup carelessly applied, her hair unkempt, but only because in the collective imaginary, people tend to associate cheap bright red lipstick, caked mascara, and holey fishnet tights (pantyhose in the US) with sluttish behaviour.
I don't think I have ever heard a woman being described as being a slut if she was generally untidy or unkempt. The word I would hear most often, in those instances, would be a slob.
EDIT 1
I'm going to play the British card now myself. I was born in London and lived there until I was a teenager, and I regularly go back to London for visits and short holidays. I was familiar with the term, slut, before moving to Italy circa 30 years ago, for me it's a well-established word whose meaning I have described above. The first definition may be found more often in books, which probably explains why the OED lists it as being first. However, Oxford Dictionaries, and The Oxford Advanced Learner's Dictionary both state that slut is:
1a) a woman who has many casual sexual partners
and list it as their first definition.
I'm certain that British native speakers today are more familiar with that definition than with its more dated one; a woman whose general appearance is unclean. I looked for references to back my gut reaction, and I looked for how the word is used today in speech, not in works of literature. I thought of The Daily Mail, a British online newspaper, right-wing, an unreliable source if one is looking for objectivity in the news but an excellent one to witness how the English language is developing. The earliest reference to slut I found in a piece dated o9/o3/2001, entitled Born Romantic
British effort of the week is Born Romantic, a comedy about various
young Londoners who frequent a salsa club. There's a well-spoken bitch
(Olivia Williams), a mousy, morbid neurotic (Catherine McCormack in
spectacles) and a rampant slut (Jane Horrocks).
They are pursued, in a
way that's hard to distinguish from sexual harassment, by a charmless,
married Scotsman (Craig Ferguson), a pathetic, incompetent mugger
(Jimi Mistry) and a self-pitying, slobbish Scouser (David Morrissey).
I strongly doubt that The Daily Mail would use a term which their readers would largely be unaware of or might confuse it for meaning an unclean, slovenly woman. The comedy, by the way and its actors are/were all British too.
I include here the Daily Mail link showing the results for "slut" starting from the most relevant. Probably there are some pieces where women are criticized for their laziness and called sluts, probably AmEng has influenced as to how the younger British speakers interpret the word today; I don't doubt it for a second, but I'm convinced that nowadays British speakers are largely unaware of its original meaning - "c.1400, "a dirty, slovenly, or untidy woman"
EDIT 2
I wish I had come across this answer posted several months earlier, further proof that nowadays British people tend to associate loose sexual behaviour with the term slut. This post I found purely by chance, but when I read the answer it reminded me of this question. All emphases are mine.
The user was answering the question “Man” is to “womanizer” as “woman” is to what?
Please excuse me if you find these terms profane but, my grandmother
would refer to woman who chases men as a slut, although this is
sometimes used to describe a girl as dirty or messy. I do recall a man
using the term to describe another who was especially open and active
in her choice of bedfellows. [...]
Jodrell May 28 '12. His profile page states he is from the UK