Portable Download

Hello and sorry if the subject is somewhat confusing.
I am at a loss in the following matter:
I teach at college and all of our classrooms are fitted with a video projector and a computer, equipment I use for teaching. Since almost anybody is granted access to the computer it is highly likely that they are not free of viruses and malware.
As of now (since the 10+ infection) I used a usb stick to transfer data for the computer in my office to the one in the classroom.
This has proven to be a constant source of trouble, anyway... I now upload the files I need on mydrive.ch to download them on the public computer. Since I erase them after class I don't care if the computer is infected or not.
So far, so good.
I use Firefox to manually log in to the mydrive-account to download my data, a time-consuming method.
Now my question:
Is there any way or any portable software I can put on a usb stick, not to download data but to get access to my account (explorer-like)? If the usb-stick is in 'read-only-mode' (no writing) the stick could not be infected and I would be really, really happy.
Sorry if this has gotten a bit longer and thank you for your help!!