I moved away from home when I was 21, but I was married and not alone. I have never regretted it. I also live in South Carolina and I highly recommend it

The first time I ever visited Greenville, SC, I told my husband, I love it there and I hope we get to live there some day. 8 yrs later he was offered a job here, and we've been here for 21 years (yes I am old LOL). I've never lived in Charleston as an adult (I lived there when I was 2

), but my husband has had some long term jobs there. And I LOVE visiting there.
I would suggest that you give Greenville a chance. It is an awesome place for young adults. It has a great downtown area, and it is very pet friendly! I take Bonnie down there often. In fact we are going downtown tonight for supper (without Bonnie this time!). My oldest is in from out of town, and we have to make a trip downtown everytime he comes home! You'll have to look at the link below and see what you think! (Let me know if you decided to visit, I have a 21 yr son that we might could talk into showing you around town

)
Greenville's Downtown
If you want more information regarding Charleston, you may want to send a PM to passionfruition (Val). She is a member here, although I don't think is online very often, but she lives in the Charleston area and would probably be a good one to get information from.
You sound like a very mature young lady, and it sounds like a good decision for you to move away from your family. Your family is always your family, and you will always have a relationship with them, but sometimes it is good not to live right up under them.
Feel free to PM me if you have any questions regarding Greenville.