How can I make a small pixel game without knowing how to code?

Scratch is worth a look if you want to start without learning a programming language. You can use visual blocks to handle movement, switch rooms and make an object respond when clicked.

Try building one room first. Get the character moving, add one clickable object, then use that as a pattern for the rest. You can bring in your existing artwork and walking frames too.

RPG Maker fits the exploring rooms and interacting with objects idea really well. It's designed for this kind of 2D game and is fairly friendly to beginners.

The catch is that it generally costs money, so check the price and any trial limits before committing. It might be the simpler fit, but it doesn't match your free requirement as neatly.

GameMaker has a free tier and is another option for a 2D pixel game. It gives you room to build the house, animate your characters and add interactions, though expect some learning rather than an instant result.

Before choosing it, check the current free tier terms for how you plan to share the finished game.

Whatever tool you pick, keep the first version tiny. One room, one walking character and one object that displays a message would prove out most of the basic idea.

After that, add doorways and more rooms. A computer interaction could just show a picture or a few choices at first, and the cat could play a sound or show a message. Those details can make it feel personal without needing to build several games inside the game.