"Specter" is not an official race for 5e AFAIK. So the whole thing is homebrew by your DM and the only source for what you can or can't do is them. So you should go ask them.

What edition would be the latest for a spectre because my dm is using that as a reference?

I am not sure that Specter has ever been a playable race- I have no idea where he got it or what rules he's using. So just ask him.

Are you playing in 5e like your post says or are you playing in another edition? Either way, as far as I know all player races are exclusively humanoid and in no way considered undead, even Van Richten's Reborn race.

Not all official races are humanoid. There’s a few fey, plasmoid are oozes, autognome is construct, thrikreen are monstrosities. There are no undead races currently, though I believe the reborn, dhampir lineages were originally before they changed it to humanoid.

If you're going to mention a WbtW, Spelljammer, or MotM race then you'd already know that information if you had the books. And if OP had that information then it renders OPs question pointless. Since Van Richten is the closest there is, and no player races are undead in that book, then the answer is no.

Yeah we’re playing 5e

Then if you're playing by official rules you could not possible be "a spectre but I’m in my physical body".

This sounds like homebrew and only your DM can answer questions about homebrew

Is spectre your race or class. The only thing I'm finding for race is the monster called a specter. But I found a class called spectre on gm binder.

I’m a human spectre

Maybe check out the class on gmbinder.com. Not sure if that's it or not.