If ggplot2 appears in the Packages pane, then it is installed. Selecting it there should not result in the stream of red output that you describe but let's ignore that for the moment. Try running the two commands
library(ggplot2)
search()
Here is the output I get from that in a new RStudio session
[1] ".GlobalEnv" "package:ggplot2" "tools:rstudio"
[4] "package:stats" "package:graphics" "package:grDevices"
[7] "package:utils" "package:datasets" "package:methods"
[10] "Autoloads" "package:base"
You can see package:ggplot2 in the list, showing that ggplot2 is loaded. Your output may look different but you should see ggplot2 listed if you successfully installed it and then ran library(ggplot2).