Hi Nat,
I've broken your post down into three issues that you're talking about and hope that I can give you a good response to all of them...
Issue 1: I feel I am not really fitting in here because I have not made any friends yet. I am always on my own going out anywhere. I have tried hard to make friends but everyone has already seemed to have found their friendship groups except for me.
You don't just make friends in your first few days - as long as you're open to making new friends, then you'll do just that throughout your university life. It's really early days and there are a few things that you can do to try and make some friends like joining sports clubs and societies, SUs have so many societies that there's bound to be one for you. Additionally your course mates might be a great source for this. It sounds like you're not feeling up to joining the conversation with people you think are in friendship groups? It's not really like school where people stick to one tight knit group, so if you see someone then introduce yourself and who knows? You might become best friends with them.
Issue 2: The subject choice I am doing seems to be better in terms of ranking and it looks better in the other uni I want to go to.
Ranking doesn't really mean all that much as a degree is what you make of it. Did you do your research for the university you are at now? How do you know that the other university is for you? There are so many factors to choosing a university that I can only guess that you've looked at it as a 'grass is always greener' solution? I'd strongly discourage transferring university at this stage, especially without knowing exactly what you're getting yourself in for...
Issue 3: I am also far away from home and if I go to the other uni I will be a bit closer to home and also to my brother in a different uni which will definitely be better for me!
Homesickness is something that every fresher will experience at some point, even if they don't admit it to anybody else. It's natural to feel this way but your family are proud of you for getting to where you are today.
In terms of if you were to transfer, you definitely would not have it done by 22nd September. You would be looking at around a week or two, that's if they have spaces and are willing to take you.
Please stick with it - you should be proud of yourself as you've made it to uni! You got the grades! Don't let this define your future or university experience - talk to lots of people and you're going to be okay!