OK, just spit-balling here to convey ONE of many possible ideas ... (it is YOUR world)
Look at a map that shows the rocky mountains or apalachian mountains running down the opposite coasts of North America.
Start with a 'Spine of the World" series of shorter mountain ranges running down the center of your world (east - west). This will not be a continuous range, but a series of mountain ranges separated by hills and perhaps a few large valleys connecting the north and south halves of the continent.
Along the south coast is a second mountain range (perhaps set in a short distance from the coast).
The rain tends to move from NW to SE across the land, creating a great desert between the two mountain ranges.
The NW coast of the land masses get lots of rain and will tend towards lush forest, swamp or jungle (based on your temperatures). Further inland , less rain falls and normal forests dominate. SE of the mountains tends to be drier with forests along the coast transitioning to grasslands further inland.
Note that the SW coast can get rainfall that misses the central mountains.
From the general terrain and patterns above, the rivers north of the spine will tend to flow north towards the nearest coast. The North will have either many rivers, or great rivers with may upstream branches. The South will have fewer and smaller rivers (less rain).
Like I said, that is just one quick option out of many - Yours (not mine) is the correct one.