You can try to rub your finish to fix your problem.
Use 400 grade sandpaper put in a hand block to sand your finish. sand it until all your nibs is gone and you get a smooth and even surface.
After that you can rub your finishing with steel wool to bring up your sheen. Then you can apply a paste wax to polish the surface.
If you sanding process cannot give you a even surface then you need to re coat with your oil.

@simoneaux I know this is an old post, but curious what you ended up doing. I just applied three coats of Pure Tung Oil + Citrus Solvent to my 100 year old heart pine and it looks really uneven and flat. Not sure if I want to sand it off and apply poly, add more and try to buff, or add a wax. Thanks!