I can’t do it without a nose clip and I never use nose clips.

I was exactly the same at first, I really just had to keep practicing until I got used to it.

I tried nose clips, got uncomfortable, air still leaked, then they broke.

I find if I started focusing on opening the throat more and sort of belly breathing, it really minimized how much I got through the nose to the point where it was no longer an issue.

Now my main focus has been breath control to the point where I can still breathe with some water in the snorkel such as after a flip turn, or just getting too low in the water, and then getting a good hard breath out to purge the water, while staying smooth in the water.

Keep at it, find what works.

A few thoughts
1- Stay relaxed, don't force the breathing. I still breathe in a pattern with a snorkel on (in, 2,3, out, 2, 3). If you're just blustering and blowing in and out randomly you're going to have a harder time.
2- Try a nose clip. I don't like them but I know a ton of people who can't use a snork without one
3- If you're getting a lot of water, are you sure your head position is ok? Are you dipping you head so much water is getting in the top? Try just floating on the wall with toes in the gutter and find a body line that's neutral before pushing off. Eyes should be about 5-10* forward.

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I wrote this, you should read it:
https://www.slowtwitch.com/...n_Swimming_6700.html