In your RDS, first check all IOPS metrics.
RDS provide a certain quantity of IOPS, and if your RDS Instance have 10GB SSD, probably your IOPS quantity is 100 IOPS (default), this value increase dependends of the instance SSD size.
If you have not IOPS enough, your RDS is blocked for IO operations, causing 'Sending Data' in your MySQL and high timeouts, but no change CPU usage or Memory, because this is an Disk issue.
For fix it, change the configurations of the MySQL, in Dashboard you change it.
I have MySQL on EC2 instance, low cost for me.
port = 3306
user = mysql
default-storage-engine = InnoDB
socket = /var/lib/mysql/mysql.sock
pid-file = /var/lib/mysql/mysql.pid
log-error = /var/lib/mysql/mysql-error.log
log-queries-not-using-indexes = 1
slow-query-log = 0
slow-query-log-file = /var/lib/mysql/mysql-slow.log
log_error_verbosity = 2
max-allowed-packet = 6M
sql-mode = STRICT_TRANS_TABLES,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_AUTO_VALUE_ON_ZERO,NO_ENGINE_SUBSTITUTION,NO_ZERO_DATE,NO_ZERO_IN_DATE,ONLY_FULL_GROUP_BY
sysdate-is-now = 1
datadir = /var/lib/mysql
key-buffer-size = 128M
query_cache_size = 128M #100M384M
tmp_table_size = 256M
max_heap_table_size = 256M
innodb-buffer-pool-size = 2G
innodb_log_buffer_size = 8M
innodb_log_file_size = 1G
wait_timeout = 10
interactive_timeout = 300
max-connect-errors = 100000
max-connections = 200
sort_buffer_size = 4M
read_buffer_size = 2M
read_rnd_buffer_size = 2M
join_buffer_size = 2M
thread_stack = 4M
thread-cache-size = 80
performance_schema = on
query_cache_type = 1 #0 #1
query_cache_limit = 128M
table_open_cache = 2680
open-files-limit = 1024000
table-definition-cache = 3024
# IOPS OPTIMIZATION #
innodb-flush-method = O_DIRECT
innodb-log-files-in-group = 2
innodb-flush-log-at-trx-commit = 2
innodb_buffer_pool_instances = 1
innodb_stats_on_metadata = 0
innodb_io_capacity = 100
innodb_use_native_aio = 1
innodb-file-per-table = 0
explicit_defaults_for_timestamp = 1
[This conf is for 2 vcpu and 4GB RAM, 10GB SSD with 100IOPS]
Work fine for me in AWS NLB + Auto Scaling Service.
Other optimizations is would be increased the innodb buffer to 50% of memory of the instance, and innodb_log_file_size with 50% of the innodb-buffer-pool-size value.
I hope help you or other users with same problem.