So first, OpenSSL has an implementation of AES-256 that’s known to be very safe against side channel attacks (Not 100% secure, take a look at CRIME, Heartbleed, etc.).
Here you are asking two things in reality : “is AES-256 secure ?” and “is using a password as encryption key secure ?”
For the first question : “is AES-256 secure ?”, so far, AES-256 is secure if you use a secure mode (I would recommend CBC but you might want to choose another one depending on the circumstances). No breach has been found and with a good implementation (i.e. OpenSSL) it’s (nowadays) unbreakable without a quantum computer which only @dloser has. Of course you can be victim of a bruteforce attack, but AES-256 use a 256 bit key i.e. there are 2256 possibilities which is +/- 1077, so from that point of view, you’re safe.
Now your second question : “is using a password as encryption key secure ?”, no it’s not. You must generate a key randomly, I’m gonna try to explain with practical examples.
Let’s consider that you use only one bytes characters in your password. With a random key you have 25632 (number of possibilities power number of bytes) possibilities which is +/- 1077 as seen above. Now if you take a password, I suppose that you use lower case, upper case and numbers, so you have 26 + 26 + 10 = 62 possible characters which gives 6232 +/- equal to 1057. While it’s still an enormous number, you just reduced your security level.
Another thing is that the password can be guess. There are a lot of other reasons, you should try to read some docs on crypto, I can recommend Introduction to Modern Cryptography of Jonathan Katz and Yehuda Lindell
Moreover, it seems that you don’t use any IV, which means that the same plain text, with the same key will give the same cipher text, which is pretty bad too. You should use a random IV, stored with the ciphertext so none can perform cryptanalysis using Known Ciphertext Attack.
I hope I’ve answered to your question. Obviously, the level of security that you wanna put in place will depend on the cost you give to the encrypted data. In one hand, if you find it too hard to put in place correct encryption/decryption and your data aren’t sensitive, it’s not necessary to raise your level of security higher. In the other hand, if your data are classified, you might want to put in place a secure encryption policy for them.
EDIT: I’ve seen the website on your profile page that I suppose you created: http://aesencryption.net/ There are at least one wrong implementation. Rijndael is an encryption algorithm, it has 3 possibles block size, 128 bits, 192 bits and 256 bits.
AES is a standard which uses Rijndael-128 (with a 128 bits block size). Rijndael-128 accepts keys of length 128, 192 or 256 bits, so AES-256 isn’t Rijndael-256, it’s Rijndael-128 using a 256bits key. Once again I hope I’ve been clear in my explanations :)
