Primer is not supposed to look streaky or have visible drip lines. While primer does not need to completely cover old coats of paint in order for your new paint to go on flawlessly, primer should be applied in a uniform manner.
Is it OK if paint primer is streaky?
YES!!!! Primer never looks good. It serves a different purpose. So calm down, don't panic until after you've applied a coat or two of your finish paint - if that looks bad then you can panic.
Does it matter if my primer is streaky?
The primer coat doesn't have to be perfect, but it should cover the surface (no bare spots) and it shouldn't be so blotchy that you get drips or visible unevenness.