Hi friend,
What you asked about removing ear wax is a common doubt of population. You can try wax solvent ear drops for softening the ear wax. But first thing is that, it should be confirmed that the symptoms are caused by ear wax. There are few other conditions which also present like ear wax, which needs different ear drops and different treatment.
Second thing is that, even after softening the wax, if it is not removed spontaneously, you shouldn't try removing it with ear buds or any other instruments. You should consult an otolaryngologist for safer removal.
Coming to second question, common cold can precipitate ear infections which cause ear pain and sinusitis which cause head ache and eye strain. So these things can be related and coexistent.
Next Steps
confirm if the symptoms are due to ear wax. if yes, you can try wax solvent ear drops.
Health Tips
never try to remove the wax by yourself. it can be really dangerous.