Is there anything that I can do about having a fly in my drink?

You can contact the company again and tell them in detail what your reaction was and any reasonable aversion you now have as to buying such drinks and see what they are willing to offer, but it will be very little. To show liability, you would have to prove the fly did not get into the drink after you removed the plastic. Since flies weigh very, very little, normally their bodies float to the top of the liquid and no one is going to notice the taste of one. So you will have a tough time convincing anyone of your story. Also, since the drink was made in an open area, it is reasonable to expect that there will be some flies around and one might get into a drink.

I presume that the fly was not intentionally put in your drink. It seems to have been in a batch that got mixed (hence the guts out) and then put into your cup. Your chances of illness are minuscule as you confirm by not getting medical care. This is a case of a defective product wrongfully provided to you which gave you emotional distress. Make an offer and litigate in Small Claims Court if you don't settle.