Been dating girlfriend for 4 months now

Problem is I house share with a girl because and saving up to buy house with girl I am dating

She won't move in with me until at least another 6 months,
Only reason I am living in with this girl is so my girlfriend can stop over because she doesn't like me stopping at hers because she lives with sister
Boyfriends have cheated on her in past and she thinks I am going to sleep with girl I live with, I feel really horrible even though I have done nothing wrong
I would not cheat on her , love her and really look after her emotionally and physically
She has little self confidence and is very very close to mam, dad and sister, feel guilty for going out with her , because sister likes her to stay in and chill with her
Plus her sister has just split up with her boyfriend and is bit jealous because my girlfriend is happy with me and we have good relationship. For 6 years when her sister had boyfriend she never bothered being with my girl friend, but my girlfriend is made to feel guilty about spending time with me by her sister

My girl friend only wants to see me when it suits her as well and is constantly putting her family before us , really love her though just wish she would trust me

Now she says she's alergic to cat so will not stop over any more , but I know allergies can be cured , but she just does not want me living with this girl, even though she has met her now, I thought that would be better but it is worse because she says I am too friendly with her


How can I try and get her to trust me ?

Her cat allergy can't be cured.
Her trust allergy can't be cured.
Her family priorities can't be cured.

... at least none of those things can be cured FOR you or BY you.

You date someone you already like to see if you would make a good match. I've only known you for 3 minutes and I already don't think you two are a good match.

What do you think?