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So currently I have several coins in exchanges and I am ready to have my address in my possession. So myethwallet isnt an exchange? Myethwallet will allow me to havey keys secure?

No it is not an exchange and I do believe so, that having been said I have not done an in depth look at myethwallet.

Here is what i can tell you for their allowed security options:
Keystore file (utc/jcon) which is a file u download when creating the wallet
Private key
Mnemonic phrase
Ledger Nano S
Trezor