I have a lot of experience with both anxiety the emotion and anxiety the disorder, as I've always been a nervous person and suffered an anxiety disorder since my childhood. Here I'm describing disordered anxiety rather than just feeling nervous, as I think that's what you're asking.
So, I experience anxiety more physically than emotionally. For me, an anxiety attack is a combination of symptoms where I feel too hot, my heart races, I feel nauseous, a sense of inescapable doom, and sometimes lightheaded as well. After a while, I'll get muscle cramps from holding my torso too tense. If I don't feel the emotion of anxiety already, I get anxious about the symptoms and it creates a vicious circle. It can creep up on me, but when it hits the only real things I can do are take my as-needed medication- propranolol, to slow my heart rate- or remove myself from the situation and have someone talk me through it until I feel calmer.
Over the years I've found other things that can help. I'm emetophobic and the nausea can trigger anxiety around that, so I have ginger sweets to take which can stop that vicious cycle where I'm anxious about my anxiety symptoms. I also have done therapy consistently for six years, which has helped a lot with grounding techniques and recognising the feeling before it gets too overwhelming. Really though, the only things which have genuinely prevented my anxiety are SSRIs, which I came off temporarily and regretted once the anxiety returned, and hormonal contraception which has completely cut the ups and downs of my cycle. I still get nervous, especially when meeting new people and particular events, but not so much I feel physically ill at the thought of it and I don't get anxious for no reason the way I used to. I can usually handle it by giving myself a pep-talk, or get through it with moral support where available.
(When I did come off those meds, my anxiety steadily increased over the months until I found myself regularly standing outside my housemate's room to hear her breathing and make sure she hadn't died in her sleep. For reference, she's perfectly healthy.)
It sounds like, from your description, that your anxiety around public speaking is a disordered feeling rather than a regular nervousness. Even though it's not every day, it's clearly something you find really difficult to the extent of making you feel ill. Something causing you this much distress and affecting your ability to live and work is worth talking about and finding possible solutions for.
Most importantly, regardless of anyone else's descriptions here and what we do or don't feel, you don't have to suffer the torture that you experience. I wish you the best, OP, for Monday and for the future in general ❤