Most kids have occasional accidents and that's why schools require a change of clothes on hand for every kid. However, I do thing 3 a day is excessive. I agree with you that she's probably freaked out by now. You're going to have to start building her confidence. It probably didn't help to read her the riot act - I'm sure you don't realize how many kids pee, poop and throw up in school! It could be some regression around the new baby, but it could also be that she has a total change in routine, has a lot of activities/distractions, doesn't always know where the bathroom is compared to her location in the class or playground (some kindergartens have one attached to the room, most have something down the hall), and she doesn't have her mom reminding her all the time. The teacher can be a great asset here but the child has to be told TO GO rather than asked if she HAS TO, you know? It may help if 2 kids go together, so find out from the teacher if your daughter has a pal she would feel comfortable around (if your daughter has major privacy concerns, then a bathroom buddy won't work even if there are separate stalls).
Do you know if she is ever actually going into the bathroom? Is she unsure of where it is or is she nervous about it? For some kids, just not knowing where the light switch is makes it scary. If she is not actually able to relax enough to fully void and empty her bladder, she may be fuller than you think. Does she have too many juice boxes in her lunch box? Too much apple juice used to send all the kids in my school to the bathroom for peeing as well as pooping. So dilute it, or give her plain water to drink. Is there a water fountain in the classroom that is fascinating her? I hate to suggest that a child not drink water, but if she's intoxicated by the novelty of a kiddie-sized fountain, she could be visiting it a lot. It's not the entire problem but it could be a factor.
Yes, you can put her in a pull-up, one of the nighttime garments for kids her age and older, or an adult garment if you don't think it will be huge and bulky on her. I'm not sure of her body type. It has to be easy to pull down though, so she can pee in the toilet and not rely on the garment.
If you think a reminder watch will work, that's one possible solution. But if she can't go when it goes off because it's the middle of circle time or during recess, it may get in the way and prevent her from listening to her body. Do work with the teacher to figure out the best times to set it for.
Our kindergarten teachers never found it helpful to yell at kids and tell them that it's not okay to do X or Y in kindergarten - sometimes kids rebel at that and feel unready for the challenges of school. If it's a really big class of kids (20+), there's just so much going on. They're learning to line up, for example - one of my K teacher friends puts a strip of tape on the floor because something as simple as "line up" is lost of 75% of the kids. They're learning their way through the building, learning names, learning routines, learning to transition from one activity to the next, watching some kids get "in trouble" for running off or not waiting their turn to talk, and so on. Find out from the teacher if there is a sticker system or other reward system, and see if "using the potty" can be a bonus thing for your daughter for the next few weeks. Not all year, but until she gets this under control. Teachers have a lot to handle with a ton of kids and too little help, but they are also experienced at problems likes your daughter's.