The reference thing isn’t the whole story, though. The brain has a natural sorting mechanism. When you first store a memory, there are a lot of details. If you use the memory, those details are reinforced. But if you don’t use a memory, the memory fades. I’m not sure of the physical mechanism, but a lot of times you wind up recreating those details from other details, and you can definitely get that wrong. While this happens a little bit early on, the longer a memory is disused, the more likely it is to happen.
Anyways, my point is that you can only think about so many things in a given time period, so, eventually information is going to disappear from your brain as you fill it up. So the storage is not infinite. You just have a built in deletion system based on bandwidth.
You could simulate this with a computer that deleted files that weren’t accessed. Some filesystems do this, although they usually have a way to set something to never be deleted. I wouldn’t call them infinite, either.
Jorges Luis Borges wrote a short story about a man who was thousands of years old and this was a problem. He remembered for example that he fought at the Battle of Stamford Bridge in 1066 England for example, but he couldn’t remember what side he fought on or why since he wasn’t even English or Scandinavian. Most of his fellow immortals who were even more ancient than he was spent their time taking very very very long naps.
A recent article in Science News describes how the brain sometimes makes new neurons when it stores memories. Not all of them, but it shows that you don’t have a fixed amount of brain memory.
Memories can have emotions attached, smells, taste, sounds, a mental state. Computers will tell you what something looked like but won’t tell you about an associated feeling. Our feelings and reactions to similar situations change over time, so our memories of how we reacted to previous situations will also be influenced by new experiences. You may think your present reactions to a new, challenging situation in your life is being handled much better (or worse) than when you were a youngster. The actual truth may be far from your truth.