Hi, Fear of public speaking is number one fear among people. It is a symptom of social phobia, but does not sound as if you have this disorder. Many people have extreme anxiety with symptoms you describe.
Medicational treatment to include beta blockers and benzodiazepines. Also SSRIs such as celexa, zoloft, paxil are used as well.
Sometimes these are enough to make you feel comfortable. You are probably aware the benzos and beta blockers are much faster and instantaneous, and the SSRIs usually take about 4 weeks to reach maximum potential.
Cognitive behavioral therapy is the preferred treatment method for addressing this issue, but there are also many online courses to address this as well.
Doing some things for yourself can help a bit such as saying aloud "I'm a little nervous" during your talk, telling a joke loosens up you and the crowd a little. Some people prefer to sit down on a stool or chair while speaking. This puts you on a more even keel with everyone, and you don't feel so much in the spotlight. As you gain more confidence you can stand up. If you are lecturing, standing in the back of the room with an overhead, allows the eyes off of you, and on to something else. Finding one person in the room who is paying attention and looks "kind" and focus on them. As you look around during your speech, focus on the bridge of the nose rather than the eyes of your audience. This appears as if you are looking directly at them, without seeing the eyes on you. You are already addressing this through Toastmasters, which is excellent. The more you practice anything, the more comfortable you feel.
One or a combination of these treatments can help you over come this common fear. Please let me know what other questions you have. Gina