Okay, I'll try to settle your nerves a bit. So it's a well known fact that most knowledgeable BMW owners emphatically state to use only BMW coolant and a mix of 50% distilled water. I'm one too, but it's not as necessary as you think. The reason use of BMW-branded coolant is recommended is because in earlier models of BMWs, use of mixing non-BMW coolant with European tap water could in some cases lead to mineral-build up in the cooling system, and over a long time period clog the radiator and other coolant passages in the engine. BMW coolant is formulated to deal with European tap water mineral content, which is why it is recommended.
This phenomenon is not as prevalent in tap water sourced in the USA. The best way to avoid the mineral build-up issue in the first place is to just use distilled water in the coolant mix. Distilled water is pure water with no minerals present in it.
In your case you've added such a small amount of coolant in the system that holds about 2 gallons total, it not a large change in the overall coolant mix, so it's not too much to worry about. I'll assume that the coolant you bought at 7-11 is regular green (non-long life) coolant, which is compatible with BMW coolant.
My bigger concern is why is your car "bone dry" of coolant. The low coolant warning should come on long before the system reservoir is "bone dry". Was the level indicator stick bottomed out and not floating at all? How much coolant did you add?
And if you can DIY, changing out the coolant is very easy on the E90. There is a DIY for it in the DIY section.