A fairly standard convention is that a man can walk 10 miles a day, horse can go 10 leagues (30 miles). 3 months is roughly 90 days. 90 times 30 = 2700 miles. 4 months is 120 days = 3600 miles. Boston to LA is 2983. Your image is 3000 pixels wide so I would say the scale is about 1 pixel per mile.

Rivers do not split as they go downstream, they join. They may go around a high place or hard rock but they join up again fairly quickly. However, in deltas they do split because they meander all over a flat plane and constantly shift their course. Think of your river backwards, starting at the ocean, as a tree...the delta is the roots, the main trunk is the main river, and the branches are all up near the mountains.

When doing lakes I would suggest first drawing in all of the rivers and then find a few places where it looks like they might pool and put a lake there...small lakes near the mountains and large lakes on the plains. To make a good looking lake, use a cloud brush in Pencil mode. If you don't know where to get cloud brushes, or how to load them into PS, or just don't find any that you like then try this:
1. New layer, fill it with black, using white draw out some rough looking blobby lakes.
2. Filter - Pixelate - Crystallize = 12. Do this again but at 6, then at 3.
3. Image - Adjustments - Brightness/Contrast = max out both.
4. Make black the foreground color. Select - Color Range = set the fuzziness at anything...black will be the color.
5. Hit the Delete key then deselect (ctrl-d).
6. Now you have rough-edged lakes instead of smooth-edged lakes.

Map looks pretty good otherwise, so nice job.