Is it ok to send out shower invitations if the wedding invitations have not been sent yet? One shower is in August and the other is in September. The wedding date is October 21st.

Yes, it's ok to send shower invitations first. Shower invitations are usually mailed at least two weeks before the shower. Wedding invitations are usually mailed six to eight weeks before the wedding (depending on if the wedding falls on a holiday, long weekend or if you have lots of out-of-town guests). It's acceptable for guests to receive wedding invitations up to two weeks before the wedding.

So if you have a shower in August, this would happen before you have sent the wedding invitations (and maybe for the Sept shower also). All showers should be held at least two weeks before the wedding (in your case, this is certainly true).