The ringing sound in the ears also known as tinnitus in medical terms can be caused due to ear wax, infections/ inflammations such as labyrinthitis etc, vascular bruit, excessive or loud noise, meniere’s disease, perilymph fistula, acoustic neuroma, metabolic disorders, heavy metal poisoning, drug side effects etc. Pressure feeling or headache could be primary such as tension headache, migraine etc; secondary due to issues like sinusitis etc or due to cranial neuralgias. It would be best to have this evaluated by a primary care physician or an ENT doctor. After a cause(s) is identified, it can be managed accordingly.
Hope this is helpful.