Pull-down faucet hose doesn't slide into sink/counter holes

Little bit of a thing here (and also my first time trying anything remotely like a plumbing project):

I’m trying to replace a leaky pull-down kitchen faucet hose. I saw it was suggested to take the existing hose to the store to compare with, but I didn’t have any luck finding the right hose at my local stores. So I wanted to replace my current hose for now so I’d have something in the meantime until I can get a new one from the manufacturer. But when I try to slide the hose back through the faucet and down through the holes, it seems like it just won’t fit and gets stuck. It did take a little extra effort to remove the hose from the faucet in the first place, but not tons.

Additionally, I tried to hook the hose up directly under the sink without going through the faucet. Again, so I could have some semblance of a kitchen sink for now. But when I turn the water on, it flows out of the hole that the hose would go through, instead of the supply hose. I’m assuming this is unexpected even though that hole would normally have the pull-down hose going through it. Is it possible that the supply hose is dislodged in the faucet, causing both problems? I’m worried that even if I do get a new hose, I might need to disassemble the faucet in order to fix whatever is going on in there.

Thanks for any help.

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