Multiple Flash Player Icons and Remote Access

I have a Macbook Air (version 10.11.6), after logging into my laptop today I found that there were 5 flash player icons on the desktop - I have auto-updates turned on, but these icons have never popped up before. I dragged them to the trash to eject them, but I'm concerned why so many would appear.

Some background of why I'm concerned, a family member fell for a scam the previous day where she gave someone remote access to one of our computers. The computer that was accessed is a very old Dell, but all computers in our house are on the same internet network.

I've always had all remote access and sharing turned off on my Mac, so I'm wondering if this is merely a coincidence or if these flash player icons could be some type of malware? Is it even possible to infect another computer through the network?