I simulate some data that might look like yours, so you don't need to put them into separate vectors. Keep them in a dataframe

Shannon.index <- runif(43,1.5,3.5)
type = rep(c("River","Lake"),times=c(24,19)) 

df <- data.frame(Shannon.index,type)

For barplot from base R, we need to calculate the standard error of the mean (sem) and mean (like you did), and we use arrows() to add the error bar:

Shannon_sem <- tapply(df$Shannon.index,df$type,function(x)sd(x)/sqrt(length(x)))
Shannon_mean <- tapply(df$Shannon.index,df$type,mean)
YMAX <-ceiling(max(Shannon_mean+Shannon_sem))

PLOT <- barplot(Shannon_mean,
xlab = "Environment", ylab = "Shannon Diversity Index", 
main = "Diversity of Parasites \nfound on Fish from River 
and Lake Environments", cex.main = 1, col = "gray80",
ylim = c(0,YMAX))
arrows(x0=PLOT,y0=Shannon_mean+Shannon_sem,cex.main=0.7,
y1=Shannon_mean-Shannon_sem,angle=90,code=3,length=0.1)

If you use ggplot2:

library(ggplot2)
ggplot(df,aes(x=type,y=Shannon.index)) + stat_summary(fun.y=mean,geom="bar",fill="gray80") + 
theme_bw() + 
stat_summary(fun.data = mean_se, geom = "errorbar",width=0.2)

You can calculate the mean and standard error on the fly, using stat_summary()

Using ggplot2 and the standard deviation to create the errorbars:

library(ggplot2)

# I'm just making up the numbers to provide the solution
mean_river <- 25 # mean(parasite_data$Shannon.index[1:24])
mean_lake <- 29 # mean(parasite_data$Shannon.index[25:43])

# To plot the error bars i'm assuming you want the standard deviation
# but you can use the min or max value
sd_river <- 0.5 # sd(parasite_data$Shannon.index[1:24])
sd_lake <- 4 # sd(parasite_data$Shannon.index[25:43])

# Instead of matrix I would use a data.frame for ggplot
Shannon_data <- data.frame(name = c("River", "Lake"),
                           mean = c(mean_river, mean_lake),
                           sd = c(sd_river, sd_lake)) 

ggplot(Shannon_data) +
  geom_bar(aes(x=name, y=mean), stat="identity", fill="gray80") +
  geom_errorbar(aes(x=name, ymin=mean-sd, ymax=mean+sd), 
                width=0.4, colour="orange", alpha=0.9, size=1.3) +
  labs(title = "Diversity of Parasites found on Fish from River and Lake Environments") + 
  xlab("Environment") + ylab("Shannon Diversity Index") + theme_bw()

This would generate the next plot:

Using the minimum and maximum value to create the errorbars:

# Example with max and min value instead of sd
min_river <- 22 # min(parasite_data$Shannon.index[1:24])
min_lake <- 21 # min(parasite_data$Shannon.index[25:43])
max_river <- 31 # max(parasite_data$Shannon.index[1:24])
max_lake <- 30 # max(parasite_data$Shannon.index[25:43])

Shannon_data <- data.frame(name = c("River", "Lake"),
                           mean = c(mean_river, mean_lake),
                           min = c(min_river, min_lake), 
                           max = c(max_river, max_lake)) 
ggplot(Shannon_data) +
  geom_bar(aes(x=name, y=mean), stat="identity", fill="gray80") +
  geom_errorbar(aes(x=name, ymin=min, ymax=max), 
                 width=0.4, colour="orange", alpha=0.9, size=1.3) +
  labs(title = "Diversity of Parasites found on Fish from River and Lake Environments") + 
  xlab("Environment") + ylab("Shannon Diversity Index") + theme_bw()

Hope this help!