No. A commercial month-to-month tenancy in FL may be terminated on 15 days notice. 13 is insufficient. [83.03] Raising the rent is in effect terminating the old month-to-month agreement & offering to enter into a new agreement at the new rent terms. Do you have a written lease? If it's for a specific term, L can't raise the rent unless the lease allows it. It may also state that L has to give a certain amount of notice before raising the rent. This is why commercial tenants should always have leases for 1 or more years.
Pay your Aug rent at the old rate, but beware -- L can retaliate for you standing on your statutory rights to 15 days notice by terminating the lease on 15 days notice. This will buy you time until 8/15 to move your business, but you can't keep L from charging more as of 9/1.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.
