LOL! And so toddlerhood begins! This is so typical for this age!
First of all, it's worth a trip to the Dr to make sure she hasn't got an ear or sinus infection (all my kids were far more uncomfortable lying down with any health issues), and check those gums for teeth. Regardless of any pain or health issues, though, she needs her sleep, and you need to break this habit with her.
Really, though, her demeanor once you pick her up says it all: this is probably all about her not wanting to be put down! Now is when you do the bedtime routine you'll be doing for the next few years- example: a last snack or feed/bottle, brushing teeth, pajamas, story, snuggle, then lights out. If you stay consistent, and firmly (but gently and with a happy attitude) do this every night, it will only take a few days, maybe a week or two to get her into a great routine.
Ignore the screams, but do reassure her that all is well- you can do that from the doorway. Don't pick her up, and don't give in.
I know it's hard- I remember crying in the hallway outside of my oldest's bedroom door, with my husband asking how much longer I was going to "torture" her... he was only sort of joking. But I knew she needed to learn to sleep, and had the wonderful benefit of the women in my family who all raised huge families (my Gram had 12) who guided me. It took a few nights, with the first lasting almost 2 hours, the 2nd and 3rd just about 30 minutes, and by the 4th night it was 10 minutes of trying to cry, but really her heart wasn't in it. LOL
Consider whether she's getting too many, or too long naps during the day, too, and cut back if you need to.
Most kids (and parents) have to learn this, and it's not fun, but in the bigger picture, it's so important to help them learn to have good sleep habits. Hang in there!