What should I do about streaks in my finish?
You shouldn't need to strip unless you scratched through to wood.

The problem with polyurethanes is that they are hard films that don't blend with the previous coat.  Other finishes will 'melt into" the previous one (lacquer, shellac, tung oil)

Your sanding, @220, was too aggressive.  Intercoat sands should be at 320 - 400.

You will have to sand back to a common level that eliminates the scratches and lines.  If you leave part of one coat and part of another coat, there will be a "witness line" .  You can wipe down the area after sanding with a soft-mineral spirits cloth and look for the lines.

Be sure you are allowing enough time between coats with the poly.