There's a really good guide to label positioning that Ravells posted, which might help you. I can give you a couple of pointers right from the current state of this map. Particularly when the line weight of your text is about the same as the line weight of features, you want to avoid criscrossing the two, which confuses the viewer's eye. Examples are the K of Kanstern and the lead parenthesis below it - both should have a little separation from the mountain symbols. It's best to avoid crossing features with labels at all, where you can. At ...Kingdom Of Nardar, you could tweak to get the O off the lake. Southern Nardan being across the river - not much choice there. Some part of Duchy Of Averia is going to cross that river, but you could at least move the word Duchy leftwards to clear the river.

The other advice you've gotten is good. I'll leave the river placement guide as an exercise for you to read through, and you can see what that would change about your rivers. The one thing I'll mention is a bit of a special case - if you do have a broad swath of swamp like you show, I'll buy it being a source for three different rivers, as being reasonably plausible. Ordinarily, if it were an outright lake, no way - it would be one outlet only. But swamps, marshes, and bogs are on again-off again land vs. water, so I'll grant there could be some slightly higher points in between those headwaters areas, for water to be flowing down from. In general though, remember any one point of water-level is going to have one or more inlets but only one outlet. Read the guide and see if that clears it up - if not we can specifically critique your river placement.

Oh, and welcome to the Guild, a couple of weeks late :-). We appreciate joiners immediately becoming contributors. You may think at this point you're totally asking, but providing a map and getting discussion going on it will teach somebody something, so you're already adding value, and thanks!