If you use any reasonably standard modern encryption scheme, there's no need to worry. Ideally you should be using authenticated encryption like AES-GCM.
In modern cryptography we generally require an encryption scheme to at least have IND-CPA security to call it secure. IND-CPA stands for "indistinguishability under chosen plaintext attacks".
This security notion is defined as a game between a challenger and the attacker. The challenger chooses a key for the encryption scheme. The attacker can then query any ciphertext of their choice to the challenger and receives an encryption that plaintext. Eventually, the attacker outputs two challenge plaintexts $m_0,m_1$, the challenger flips a random bit $b$, and gives an encryption of $m_b$ to the attacker. The attacker can continue to make queries as above and eventually has to guess which message was encrypted. In an encryption scheme that is IND-CPA secure an efficient attacker can essentially do no better than guessing randomly.
The attack you are worrying about is much much weaker than what we consider the minimal security required of an encryption scheme. Any sane implementation of AES-CBC, AES-CTR or a modern stream cipher like Salsa/Chacha would be secure in this sense. (Even 3DES in CBC or CTR mode is fine, though horribly slow.)
In practice malleability of ciphertexts is often an issue, which is why it's generally advised to use "authenticated encryption", which prevents any modifications of the ciphertext.
