Im glad flex clarified the air embolism myth...I was just getting to it myself. It would take a VERY large amount of air introduced into the vessels to cause a catastrophic event that you hear about in these horror stories. Funny, as a nurse, when our IV pumps alarm with the message on the pump saying "air", people get thrown into a panic. It's a very common misconception.
The blood clot worry is also unfounded. You are talking about a collection of fluid superficially. That is not consistent with a blood clot.
As for the OP, I totally agree that this sounds like a textbook "miss". Other than being a little painful and unsightly, it won't harm you as long as it continues to improve. The liquid that you missed the vein with that ended up in the subcutaneous tissues will eventually be reabsorbed. Warm compresses, elevate the extremity, and keep an eye on it. You said it is already showing some improvement, so that's good! If it starts to worsen, becomes red, warm to touch, starts draining, or you run a fever, then you need to be seen by a doctor.