The key length does not impose a limit on the message size. The message can be as long as you want, and your 128-bit key (nonstandard for DES?) will still be good. The DES cipher operates on blocks of bytes, one block at a time. Standard DES uses a 56-bit key (plus 8 parity bits) and 64-bit blocks.
should I encrypt each 16 chars alone
then concat them, since my master key
length is 16 bytes?
Ciphers in general do not require the key and block sizes to be the same; they can define complicated operations taking a given block of cleartext and transforming it with the key to a block of ciphertext (usually of the same size). When multiple blocks need to be encrypted, a mode of operation is specified to describe how one block relates to the next block in the process.
When operating in the electronic codebook (ECB) mode, the message is divided into blocks, and each block of cleartext is encrypted separately with the same key (the resulting blocks of ciphertext are then concatenated). Like other modes of operation for DES (i.e. CBC, CFB, OFB), this approach has its pros and cons. You will need to pick the mode most suitable for your application.
Btw, you should also be aware that DES is now considered insecure.