From what you’re describing, it appears you have a specific phobia that causes you anxiety. Physiologically speaking, this is most often due to a hypersensitive sympathetic nervous system; the public speaking is triggering a fight-or-flight response causing your heart to race, your mind to become hyperaware of your surroundings, and you to sweat.
For situation treatment, a low dose short acting beta blockers such as propranolol taken 1-2 hours before speaking in public has been found to be very effective. Alternatively, a low dose short acting benzodiazepine such as alprazolam can also be used 1-2 hours before speaking in public. If the public speaking and presentations are regular, patients often adapt and long term pharmacotherapy is usually not necessary.
In addition to pharmacotherapy, patients have also been shown to benefit from psychotherapy which involves addressing the underlying issues that cause the specific phobias.