I learned in elementary school about 20 years ago that we'd run out of oil in 20 years. Kids today probably learn the same thing and kids 20 years from now will probably also learn we have 20 years left. I don't know where that popular - and erroneous - "factoid" comes from (hippies: got to be the hippies).
In all probability, we have 50 years before we start feeling a sqeeze with supply not growing fast enough for growing demand and in 100 years, we'll start having real problems keeping an oil-based economy going.
Your teacher is correct about hydrogen, but should elaborate: hydrogen is just a medium for storage. Its the chemical inside a certain kind of battery. People talk about getting it at gas stations and that makes it sound like gas, but you could charge your car's battery much the same way if you wanted to.
Hydrogen releases energy when combined with oxygen. The product of the reaction is water. Hydrogen is manufactured by using energy to split water. As you can see, manufacturing and using hydrogen use the same reaction in opposite directions, so the energy given is the same as the energy put in. In short, you still need a conventional power plant to make the power to make the hydrogen. In the US, that means that hydrogen power actually comes from coal (50%), nuclear (25%), etc. Not an improvement as far as economics and environmentalism is concerned.
All that said, hydrogen may one day replace gas in your car, but only after that first half of the electric power grid is converted to something besides coal - and given enough extra capacity to handle making all that hydrogen.