SharePoint 2013 Alternate Access Mappings to add additional external and internal URL

I'm very new to SharePoint administration.

Here's my scenario.

I have a sharepoint, that I'm migrating. I'll call the current sharepoint "oldsharepoint", and the one I'm migrating to, "newsharepoint".

The oldsharepoint is currently accessible from inside and outside our environment by going to sharepoint.mydomain.com. I eventually want that URL to go to our newsharepoint, but for now, I just want to set up an alternate URL to our oldsharepoint. For example, I want to be able to go to sharepoint.mydomain.com and oldsharepoint.mydomain.com and they both go to my oldsharepoint.

I've already added the NS records to my external DNS as well as my internal DNS, but they just spin, which makes sense. I found the Alternate Access Mapping, and here's what it looks like (except the port isn't actually 120):

https://externalsite1.mydomain.com | Default | https://externalsite1.mydomain.com
https://externalsite2.mydomain.com | Default | https://externalsite2.mydomain.com
https://sharepoint.mydomain.com:120| Default | https://sharepoint.mydomain.com:120
https://sharepoint.mydomain.com    | Default | https://sharepoint.mydomain.com

I'm guessing if I just added another two lines, like these below, it would work, but I really don't want to break our current setup, just add another URL that goes to the same thing.

https://oldsharepoint.mydomain.com    |Default| https://oldsharepoint.mydomain.com
https://oldsharepoint.mydomain.com:120|Default|https://oldsharepoint.mydomain.com:120

Is that correct, assuming that I have the DNS records set correctly? Or will this break my current setup?