Well, I haven't started HRT yet, but may I offer some opinions?
First off, your sister saying you don't look any different, honestly, isn't really basis for how you are perceived. If you look at your lawn every day for a year, chances are from day to day, week to week even, it may not look different. But, if you take a picture of it, and then wait maybe 4 months or so and take another picture, chances are it will be different. If you're in constant contact with her (daily, weekly, even bi-weekly) it's probably going to be hard for her to see the changes. Even as learning said, our changes take years, and some of us are more gradual than others. If other people are gendering you as female (aka people who don't know you, or you don't see often) I wouldn't put your sister's opinion high on my list.
My other opinion I must apologize for first, as I'm not trying to attack anyone. But, your sister sounds like one of THOSE lesbians (at least, I got she was lesbian from your hints). One of those lesbians who doesn't think trans people are right. Like we're gay, and we're just trying to find a way to make it more acceptable or something. You know who I'm talking about I hope. There are just some GLB people out there who think T isn't a real thing, and don't accept us just like many other cis people don't. Perhaps that's her opinion, perhaps not. I'm just guessing.
All in all, if you have other supportive people, take the positive and ignore the negative. Sure, she's close to you, but how good is family who is against you? My in-laws considered me "family", but dropped me under the water with a 2 ton boulder tied to my feet when they found out I was trans. Is that really family? I don't think so.
Stay strong. Remember you're beautiful, and if you have passed in public already, you're already ahead of your sister's opinion.