df <- merge(df,df
  ,by.x=c("from_id","to_id"),by.y=c("to_id","from_id")
  ,all.x=TRUE,all.y=TRUE)
df <- mutate(df,Messages_sent.x=coalesce(Messages_sent.x,0),
                Messages_sent.y=coalesce(Messages_sent.y,0))
df$row <- 1:nrow(df)
rbind(select(df,-Messages_sents.y) %>%
        rename(Messages_sent=Messages_sent.x),
      select(df,-Messages_sent.x) %>%
        rename(Messages_sent=Messages_sent.y,from_id=to_id,to_id=from_id)
     ) %>% arrange(row) %>% select(-row)

df <- data.frame(from_id=c(624227,624227,624227,624227,624227,624227,667255,667255,667255,7134655,713465),
                 to_id = c(352731,693915,184455,771100,503940,91558,626814,857601,862512,156874,419242),
                 message_sent=c(1,6,2,1,1,1,2,7,3,1,1))

#create another dataset where from and to columns are switched
df.swap <- data.frame(from_id = df$to_id, to_id=df$from_id)

# merge 2 together
df.full <- merge(df,df.swap, by=c("from_id","to_id"), all=TRUE)

# fill missing values with 0
# those records will correspond to all the pairs where
# someone did not send any messages back
df.full$message_sent[is.na(df.full$message_sent)] <- 0


#create a unique ID for each pair. This can be down various ways. One easy way is to
df.full$pair_id = sprintf("%06d%6d",pmin(df.full$from_id,df.full$to_id ),
                                   pmax(df.full$from_id,df.full$to_id ))

# calculate total time for each pair:
total.time <- aggregate(df.full$message_sent, list(df.full$pair_id), sum)
names(total.time) <- c("pair_id", "total_sum")

# if this total time needs to be a part of the data.frame you can merge it back
df.full <- merge(df.full, total.time, by = c("pair_id"), all=TRUE)
head(df.full)
#         pair_id from_id   to_id message_sent total_sum
# 1  091558624227   91558  624227            0         1
# 2  091558624227  624227   91558            1         1
# 3 1568747134655  156874 7134655            0         1
# 4 1568747134655 7134655  156874            1         1
# 5  184455624227  624227  184455            2         2
# 6  184455624227  184455  624227            0         2