Is it supposed to look like that?

Sharon
OK so yesterday I had to do a 2-hour glucose test. In the middle of it was my OB appointment. So they get the heartbeat for my little girl (140) and they measure me. I'm measuring exactly where I'm supposed to be. I'm almost 28 weeks and my next appointment is schedule for 3 weks from now so they gave me the normal T-DAP and Whooping Cough vaccine. No problem. The Dr. Asked which hand I write with and I tell her my right so she gives me the shot in my left arm. Just from that, I'm expecting that my arm will be sore or something. So it is.. It's sore to touch and lifting my arm over my head is uncomfortable. No big deal. When I was about to shower today I looked at my arm and noticed that it's kinda red. It looks like there's a sideways red T on my arm. The shot was given right in the middle at the crossing point. I touched it and it feels hard under all of the red area. Not even in a circle around the shot. Just under all the red. Is this normal? The last time I got shots was 5 years ago when I was pregnant with my son so I don't really remember much about them. So is it normal to have this oddly shaped red area around the shot? And is it normal for the red area to feel hard?