Working-out Wrong?

biceps arent even assisting muscles in the benchpress.. you might be putting your arms too far to the side causing your biceps to overstretch and it'd be causing you a small amount of pain. you should try using a barbell since you're a beginner + it will be alot easier to build foundation strength and then you could work with dumbells later for a bit more stability and balance.

It wasnt a pain, more like a "wow these got worked today" feeling. Even when we are working our back, I feel it so much in my bicep and not at all on my back. It's kind of annoying because I think my arms are going to get huge and my chest is going to be a fluffy bunny. I was doing the exact same motions as him, he even stopped to watch and make sure I was.

Is it possible that my arms are so underworked that they are feeling everything, as upposed to my chest/back.

Speaking of feeling "tight," that's usually called a pump if it comes after a few tough sets. Pumps are usually what gym rats aim for when they workout.

The trainer I worked with one day said he judges how good he did at the gym on how well he can drive his car on the way home.

It's completely normal.