Popcorn, I think there are all kinds of possible explanations:
1. She just wants to be friends with you.
2. She had traumatic experience with men (as Zetigrek wrote) and that's why doesn't want to be touched and doesn't want to explain why she doesn't want to be touched.
3. She's using you (a room for free, food for free).
4. She's a virgin or she's ashamed of her body (but I don't know if that's the case as you wrote that she's "sexy").
5. She doesn't believe you have feelings for her and thinks that you tell her bs just to have sex with her.
6. She's a lesbian and she's not aware of this lol ;)
I don't know any other Polish girls, is it cultural maybe?
I don't think so, not to such an extent.
Judging by what I read here on this forum Polish people are not as easy-going and open as Americans. But holding hands for a couple in Poland is pretty normal. There are people who may find it childish and laugh about it. But it seems she doesn't want anything that can be associated with a romantic relationship.
So it looks like she doesn't see you two as a couple.
I am a bit of introvert myself, but I would behave like her only in such situations, I guess:
- when a guy is too fast for me, and I need time to decide what I want,
- when I think that a guy is doing some sweet talk just to get me into his bed,
- and when there's no physical attraction and I have problems with saying this to a man as I don't want to hurt his feelings, because I like him.
Four months for some people maybe enough time, for others - not enough. It's really hard to say, as I don't know this girl.
I think some more info would be useful, like:
- when she moved in to your place, was she already aware of your feelings and your physical attraction to her?
- how old is she? What's the age difference between you two?
- does she have a job, any money?
- did she have any boyfriends before?
- how good is her English?
She should know better than to take me that way
Are you sure? How long have you known each other?
Access is the issue here. You suggested teasing and some cheerfull drink. Ok. I'm taking that seriously.
I think you should simply confront her, tell her that you don't understand the situation and what is it that she wants. Being friends or romantic relationship. Maybe she will be more relaxed after a drink and will be more talkative. I don't know if trying to touch her when she's tipsy is a good idea. She may understand this in the wrong way - that you want to make her drunk and more "accessible" (and it kinda looks like it).
The next phase I just laughed with her about it.
Then maybe don't laugh about it anymore, talk to her and tell her how difficult this situation is for you. Tell her that you prefer her to be honest with you.
That's my two cents ;)