Wow, you have seven classes a day? We have 4.
Anyway, to the issue:
Go to the bathroom, get a drink, etc. during lunch and in earlier classes. Don’t stop for anything on the way to 7th period. If you drop your things, or fall down the stairs, or something else inevitable like that, be sure to let your teacher know, I’m sure he/she will cut you some slack if it was something you couldn’t control. Don’t stop to talk to friends, you can say hi if you pass each other on the way, but don’t stop to talk. Don’t stop to talk in the locker room either when changing clothes etc, just change your clothes, brush your hair, etc, and get out as quickly as possible so that you can get to your 7th period on time. Try to use the least crowded stairway, often in high school, the longest way around is actually the quickest.
If you’re really having too much trouble getting to class on time, talk to your guidance counselor to see if you can get your schedule re-arranged so that your classes are closer together when you have them.
I wish you the best of luck, I just started high school today as well. Luckily, all my classes are on the first floor except for my last period.