Well at this point it's hard to say what is secure and what isn't. If you ask me, nothing is secure! There are always ways of manipulating things which is not yours. Some things are harder than others but the answer remains.
I woudn't be worried of any brute force attacks as any brute force attacks would require multiple months before finding the username and the password combination. You may want to change your password to not a dictionary word and a combination of both letters and numbers. The lazy way of doing a brute force attack is known as a dictionary attack, this would take words of the dictionary and enter them until it matches to the password, if you're password is not a one word password then you should be fine from brute force attacks.
I will tell you this, MYSQL is the largest opensource database software in my opinion and by far the best and user friendly. The reason forums like
vB, phpbb3 use mysql amongst others is because it is secure enough for any business or website out there.
also to for security reasons you should always encrypt passwords before inserting it into the database.
So your answer is yes, mysql is secure. I woudn't worry about it too much.