Is my anger justified?

Context, I joined this company 4 months ago. I'm still an associate level.

My director has been asking me favors here and there, but most of them has been work related (he asked me to look for a moving company to move office bc we were going to relocate). I understand and even if it isn't my job to do those things, I did it bc it's still the benefit of the workplace.

But just now, he asked me if I could carpool an intern that'll join in June. Now, with the new relocation, one way drive is about an hr and half to two hrs. If I stop by to pick up this intern... it adds 30-40 min just one way. So I will be sitting in LA traffic for 4-5 hrs everyday. Why the FUCK would I want to do that? And all I get is gas money? What about the additional time I sit in traffic?

I hate how I'm the target to ask this. This intern is apparently a daughter of a big client. Idc who she is, I ain't giving up my time and money. I feel like my director is trying to take advantage of me bc I would try to help everyone in need, and I feel pressured to do so since I'm new. But being asked to do this pissed me off so much, idk why I'm so angry about it. Made me want to quit this job.

tldr; My director asked me (an associate) to pick up and drop off an intern, that he has personal connection to, 2-3 times a week to work. This adds 40 min ish to my commute one way, and all I get is gas money.