I'm stuck

[Dracula]

So while i was looking up how to get the armor key without getting killed i found that first i need to get the imitation of a key,and for that i need the dog collar. The problem is that i can't open the door to the dog that wears the collar due to using my 2 old keys to open other doors in the mansion. I've searched everywhere and can't find another old key.

The only key left in my inventory is the sword key which i've used to open a door,or maybe 2 i don't remember. Do i need to start a new game?

[James.Havoc]

If you still have the sword key, then there is most likely a room left, where you can find the old key you need right now.
Usually there is one door (that requires the sword key) that overlooked quite often. Its the one that leads to the kitchen. You'll find the door at the end of some stairs which are located at the eastern side of the very first hallway, that can you enter in the game. (The one, where you meet the first zombie).
And in that kitchen is an old key.
The other two are in the bathroom where you can drain the water from the tub and get attacked by a zombie and in the save room in the easter staircase.

And iirc, there is only one way in this game, where you can softlock yourself if you collect the wrong items in the wrong order. And if you have the sword key already, you are way past that point.

So....no, you dont need to start a new game.

[SoulReceiver]

As others have said, it's not possible to block yourself from progressing when it comes to keys. There are enough accessible Old Keys in the mansion for you to open all necessary doors. If you need some help on finding where these are, there is a guide here that shows them: https://www.evilresource.com/resident-evil-remake/items/old-key