I am a high school student in the United States. Recently, some teachers at our school will not permit students to use the bathroom during class because it will disrupt students’ concentation; not taking into consideration how urgent the need is. Is there any Halacha that approves/condemns this behavior?

The Shulchan Aruch OC 3; 17, says you are not allowed to hold yourself. I am sure your teachers are aware of this Halacha, and if you will convince them you are trustworthy to say you need to be excused, they will treat you accordingly.