Was I actually arrested for a DUI if they didn't take me to jail and didn't give me any paperwork?

I was at a gas station around 12:30 am to buy cigarettes. There were 2 squad cars there and the officers were talking outside the cars. I got in the vehicle and put the car in reverse and turned the lights on. I noticed the interior dash lights were very dim. Being unfamiliar with the car, I put it in park to adjust the interior lights then put it in reverse again. The officers walked over to me and asked me to put it in park. He said, "It looks like you're having trouble shifting." I explained what happened. He said he could smell liquor in me and asked me to step out and take a field sobriety test n breathalyzer. He asked if I had any injury or disability and I told him yes, I had a hip injury. I stumbled on the line because it's hard to limp on a straight line. They didn't say much about and have me a breathalyzer, which I blew over. They told me that I was getting a DUI and put me in cuffs. They took me to the hospital for a blood draw put me back in cuffs and just took me home where my boyfriend had to sign something and they removed the cuff and I went in the house. They told my boyfriend to walk down to the gas station, which was only 5 blocks away, and pick up the car. That was it.