My daughter is currently in a SwaddleMe and has recently begun to wake herself up by getting her hand out and playing with her face This was always a slight problem but since she has started to seek her fist to chew on, it has increased exponentially. I have the SwaddleMe as tight as it can go and she can still break out of it. Is there anything more I can do to keep her hands in?
It sounds like she has developmentally outgrown the swaddle and is ready for a woombie or similar one piece jammy cacoon. It zips up and provides more room for movement while keeping baby in a comfy pacifying swaddle.
A similar effect can be obtained with a traditional square cloth swaddle by tying the ends in a knot around the chest.
I agree that your daughter may have outgrown the swaddle you're using. However, my own daughter is only a month old and can work her arms free of a SwaddleMe or a Halo SleepSack Swaddle given a few hours, unless the swaddle is drawn up very tightly.
I disagree with some of the comments; tight is not necessarily bad. You certainly don't want it loose, because then they just break out of it. Most parents do not swaddle tightly enough, leading to this problem. A "tight" swaddle has enough room for your child to breathe comfortably (it doesn't take much) but keeps their arms pinned. Contrary to initial fussing, babies feel comfortable when swaddled very firmly.
If your daughter is old enough to have conscious control over her arms (as in when you put her in the swaddle she will actively and intelligently wiggle her arms free relatively quickly) then she has probably outgrown the "arms-in" swaddle method in general. If not, then I would focus on tightening the swaddle around her shoulders; that will allow some movement and keep her abdomen free to breathe, while restricting her ability to actually get her hands out the top of the swaddle.
You may also try a swaddle with a different material. Most swaddles including the SwaddleMe brand are made with a fabric that will stretch relatively easily. While these fabrics are nice and soft to the touch, the stretching can limit your ability to get the swaddle as tight as you need. Complicating this with the SwaddleMe brand is that the hook side of the velcro is just a couple square-inch tabs, so there's more limited adjustment range.
By contrast the HALO SleepSack swaddles have long strips of the hook material that can securely adjust over a very wide range of tensions. However, the HALO brand aren't designed for use with a 5-point harness (and you should not attempt to use them when the child must be harnessed). We use both regularly, but generally prefer the SleepSacks when she's not in a carrier or car seat.
In either case, a swaddle made of a stretch fabric can stretch out over time. The SleepSack we got from the hospital is especially bad; it's "newborn" size but when she's wrapped firmly in it the velcro doesn't meet up. We have two other SleepSack swaddles, one exactly the same but issued from a different hospital and handed down to us, and one made of a microplush material that isn't near as stretchy. Both of them provide a much more secure swaddle with less stretch and more positive velcro contact, and we generally prefer these when putting her down for the night.