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Is this the way it should look?
If that is the look you wanted to achieve, than yes.
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Did I do something wrong?
Not necessarily, there are many ways to doing things.
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Am I suppose to do something afterwards?
Again, that all depends on what you want it too look like.
Don't think that these comments are meant to be rude or less than helpful, on the contrary. I'm trying to help you look at weathering a little differently. There is no right or wrong to any of this, there is only the outcome that you strive to achieve. Does this match your reference photo or what you see in your mind?
Since you applied these pigments with water, you should be able to use a stiff dry brush to soften them or remove some of them. You could also dampen your brush (not soaking wet, just damp) and go back and slowly re-shape what you have. You can remove it where you don't want it, make downward streaks where you want to show where rain water has washed some away. You can further blend them and remove the more harsh tied marks etc. You can go back and add more later where you want more or maybe took too much off.
Weathering is not a simple linear process like many may think, going back and forth between mediums and applying and removing effects is far more important and creates a much better finish than adhering to some 1-2-3 process.
Switch your focus from being right or wrong and apply it to trying to mimic things you see in the real world or your reference photos. Almost nothing you do is permanent and can almost always be lessened a great deal or taken a step or two further.