Wtf am I supposed to do at this intersection?

I just moved and started driving to work. It's an easy drive except for this completely bizarre intersection where I am getting honked at every morning. Please help me figure out wtf I am supposed to do.

Here is a MS Paint diagram I made of the problem (I hope r/dc likes these as much as r/legaladvice does). So basically I am going northbound on this road, and it comes to a traffic light. A pale green bike lane appears between the two lanes. Before you get to the traffic light, there is a sign that says left lane turns left, right lane turns right; there is no option for straight. However, the road arrows have the right lane as both a straight and right turn lane. It's important to note here that this garage driveway I am trying to get to did not exist until 2 or 3 years ago, so it's possible that the sign stating they are only turning lanes are older than that. Anyway, I have been using the right lane in the mornings to go straight into the garage entrance, as seemed the logical thing to do with the straight arrow in that lane. But every morning the traffic light turns to the green right turn arrow and everyone just lays on their horn at me since I am preventing them from turning. But I am going straight and there is traffic turning left from the perpendicular street so it's not like I can go anywhere. So everyone just gets pissed at me because they are missing their light and I feel bad.

Am I correct in using this right lane to go straight? Is there somewhere else I should be stopping, or something I should be doing to let people through that I'm completely missing? Please help, I don't like other drivers getting mad at me!