My sister is currently in the same boat as you. Since results day, she's been extremely anxious and upset about the prospect of leaving home. Sometimes it's hard to believe when people tell you that everyone's in the same boat, but you are, it's just that everyone responds to and copes with that feeling differently and some feel it more extremely than others.
It's really important to do what is right for you individually.
There are so many ways I can reassure you about going to university and leaving home. I found it really hard at first but eventually uni becomes a home away from home and stops being scary. A lot of changes happen in the transition from school to university and they can feel really intimidating before you go. Please know that what you are feeling is completely normal.
If you feel that a gap year is what's best for you, then take one. No one will judge you or think less of you for it. If you feel like you'd be just as scared and anxious after a gap year, then try going to university for a term and seeing how you get on, if you hate it, then it probably isn't right for you and you can leave and try again next year. It's important for you to know that you will always have an escape. No one is forcing you to stay there forever, your life is in your hands. I would recommend trying to stay there for at least the first two weeks, then if you still really want to go home, you can. No one is stopping you but yourself. You might miss out on things at uni, but at the end of the day it's your personal choice. If you're worried about making friends, the short answer is: don't. There are so many students on campus that you are guaranteed to find someone who has similar interests to you. Join societies and fill up your time with extra curricular activities instead of worrying about home. Make the most of your time there because it's really over in an instant.
Know that you won't actually be there for long, three years sounds long, but factor in the month-long holiday breaks and early summer and your academic year is almost less than half a year. It may help you to research anxiety on the NHS website and elsewhere as there are lots of effective ways of coping with it and looking at the feeling as something treatable can help you to relieve some of the stress and worry.
Stay calm, keep busy, and buy some photo frames and posters to make your room your own. It will only feel unfamiliar for a short time, and you'll always be in contact with your loved ones. <3 Hope this helps you!