Paths to local site?

Hello! I have been working on a site locally on my computer, using WAMP. Somehow, the path I use to direct to my main site homepage has always been (for example) mylocalsite.loc/mylocalsite. Ideally, it should simply be mylocalsite.loc (which at the moment this leads to localhost…?)

I can’t remember which instructions I used to install, but I assume it was something I did then (I have not had any other problems at all).

Other than that the actual functionality is fine, and this has only started to matter when I’m adding in links etc – which at the moment are mylocalsite.loc/mylocalsite/link, when of course they should be mylocalsite.loc/link in anticipation of eventually being moved to a live domain. Obviously, I don’t want the link paths to end up being mylivesite.com/mylivesite/link.

What I need to know is whether this is a big or small thing to change? How much does this matter in the long run – will it affect the transfer to live anyway (which from what I understand involves changing/updating paths)? I’m assuming it means going into my database, but I cannot risk losing ANY of the work that I have already done – I must stress this – and this is the first WordPress site I have worked on.

I would be very grateful for any safe, straightforward information or instructions you can provide. Thank you.