As you have just discovered, Superglue is called that for a reason. It causes a very strong bond very quickly. In fact, it is so strong and fast that we use a modified version of it called Dermabond in surgery
all the time! So the short answer is no, you likely do not have anything to worry
about. Superglue tends to be cyanoacrylate based which is fairly hypoallergenic to begin with, so the risk of an allergic reaction (while not zero) is fairly minimal. Superglue tends to dissolve over time with frequent movement on live skin so it should come off by itself in a couple of weeks. Things you can try to do to speed it up would be to scrub your hands gently with a pumice stone when you shower, and you can also try using an acetone-based solution like nail polish remover. Do NOT apply it with cotton, however since cyanoacrylate can react strongly with it. I also wouldn't recommend using it if you have cuts or open wounds on your hands.
If you notice any swelling or redness in your hands, loss of strength or sensation in areas other than below the glue, if the superglue does not come off after a couple weeks, or if you want it off sooner, you should see your primary care doctor
who may have more in their arsenal in terms of removing the film. Oh, and remember to wear rubber gloves next time!