Whenever I step on the gas hard to get around someone or to merge safetly, I smell something burning like bad brake smell, but it's not the brakes. What could it be? It goes away after several minutes of normal driving.

Automatic.

Ok, you may be smelling your exhaust. There is a sulfur smell that is emitted when high load is demanded from the engine, and this is because raw gasoline is being burned in the catalytic converter. It will dissipate as soon as all of that raw fuel is burned and the fumes are cleared from the exhaust. Otherwise, I wonder if you are smelling a slipping/melting drive belt... Check the drive belt for wear, cracking, fraying on the sides, and listen closely for any chirps or squeals when you press the gas hard. Squealing and chirping under power will indicate a failing drive belt tensioner as well.

Thank you Casey! If the drive belt and tensioner are fine, is the sulfur smell from the exhaust a normal thing, something not to worry about under those high load situations?

No problem. The sulfur smell is normal when driving at normal speeds, then hitting the gas hard, then driving at normal speeds again. Your check engine light will pop on if there is an issue with the air to fuel ratio, so no worries there. With this as the only symptom, if the belt and tensioner are OK, I recommend monitoring to ensure you don't smell it any more frequently. You could find a back road, let the engine heat up, drive at a normal speed, hit the gas hard and then stop the car (leave the engine running). If the smell coming from the exhaust is your smell, you know you're OK.