It can affect your BG at the time and therefore the HbA1c, but baring in mind the HbA1c is a sort of 8 - 12 week average, it could be difficult to work out how much having the infection affected the overall HbA1c.
I think there is a tendency to dwell on numbers and I personally liken it to losing (trying to lose in my case) weight. Being concerned about the number achieves nothing, especially when there is a possibility that something like an infection and medication has upset the result to a degree that can't be quantified.
Here's to your next HbA1c.
BTW, an amusing story, sort of. We are lucky enough to have a cleaner for a few hours a week and we have no problems if she wants to stop for coffee, have a chat, weigh herself, take her BP etc (sometimes I think she lives here LOL)
The BP meter is 6 weeks old and subtracting the number of times my wife and I have used it, she had used it 48 times in 6 visits. So an average of 8 times every week when she's with us for a couple of hours, 8 times a visit. I don't mind what she does, she does what she has to do so no problem. Except continually taking your BP over a couple of hours isn't a great plan so I just hinted that although I don't mind how often she uses it, maybe just once per visit was enough. She then told me that she has to do it several times in different positions to get the lowest result which evidently is when she's flat on her back on the floor. The instructions do say that you have to be seated with your arm and the cough at chest height. I did ask how much of the day did she lie down to keep her blood pressure down to a number she felt happy with.