“What can I do to overcome my fear of heights?”

Behavioral therapy may help

Fear of heights is one of the most common phobias. It is very treatable and responds well to cognitive-behavioral therapy (CBT). You should get an evaluation and CBT from a psychologist who has experience in treating anxiety disorders.

One can combine relaxation techniques with guided imagery that is associated with the phobic situation. First begin by imagining the height that triggers your fear. Focus on your anxiety response to the height as you imagine. For example, can this imagery trigger on a scale from 0-10 where 10 is the most anxious a 9 or 10. If so let your anxiety register and then begin the relaxation by breathing sequential muscle tensing and relaxing and imagining being in a relaxing peaceful place. Once you replace the anxious imagery with this soothing peaceful imagery you have begun the process of mastering the phobia. Now you simply practice this sequence over and over to gain a sense of agency over the phobic situation. When you feel you have agency you can go to a real height and use this intervention

Behavioral, desensitization therapies are usually the most effective treatments for phobias such as this. Seek a consultation with a recommended behavior therapist. Ask your PCP.

It may be something that you cannot ever. Try little by little getting close to heights. When or if you shake and sweat and get dizzy, stop and stay away. Some get vertigo later in life or after an accident. It sounds like you have that.

Therapy could help you. Hypnosis also could help.

Go to this link. It may help you.
https://www.psycom.net/acrophobia-fear-of-heights/