Unfortunately you'll have to rethink how your drawings connect in order to solve this problem. This means taking a look at what you're trying to represent and then understanding how vector graphics draw connecting lines that form fillable shapes.
Most vector apps do this in a kind of similar way, but it's very confusing (at first) because your preconceived notions of how drawing software might (or could or should) work are going to be different from the way they actually do.
Unfortunately this problem is for everyone coming to vector illustration from a creative perspective because it's essentially a collection of mathematical equations that define these curves, rather than some consideration for how end users actually think of lines.
There are a couple of applications that think more along the lines of end users illustration (real world) techniques, but InkScape is not one of them.
Inkscape uses what's considered the classical vector style of "drawing" in which lines are essentially just primitive exposure to the underlying mathematics that defines where those lines go, how they curve and who and what they're connected to.
In order to best understand this, I'd strongly suggest taking the time to watch a few videos on vector drawing in Inkscape so you can thoroughly perceive the nature of vector illustration in this "classic" methodology. It's kind of clunky, and will seem very odd, at first, and won't be anything like how you imagined drawing on a compute might actually be.
This guy doesn't mess around, and gets right to the meat and potatoes, watch his two videos and you should be almost set:
Then, if you really don't like that approach, have a look at this, and feel sad, because this wonderful app has been abandoned:
However its inferior cousin lives on: