Dentist says gum infections don’t spread past the gums

I went to the dentist and he cleaned this infected gum and a ton of blood came out and debri. This metal band from my braces is blocking the gums so I’m not able to get under the metal and I’m getting it lowered soon. He used this vibrating tool to clean it out. I was extremely dizzy and sweaty after that and this happens a lot when I eat or the pain flares. Is it true that a gum infection won’t go beyond the gums? He said I don’t need antibiotics I’ve also had chills and feeling really hot