When using ElGamal on elliptic curves you have two possibilities:
Encoding free Version of El Gamal
Use a version of ElGamal such as "hashed ElGamal" that avoids the task of mapping
messages to points on the curve. In standard ElGamal on elliptic curves you would compute
the ciphertext as $(C_1,C_2)=(kP,M+kY)$ where $k$ is a random integer, $M$ the message $m$
mapped to a point on the curve, $Y$ the public key and $P$ the generator point.
In hashed ElGamal, the ciphertext is $(C_1,C_2)=(kP,m\oplus H(kY))$ where $H:G\rightarrow \{0,1\}^n$
is a hash function that maps points on the curve to $n$ bit strings. Consequently, you can encrypt $n$ bit
messages, for instance 256 bit if you use SHA-256 for $H$. For the input to $H$ you need to encode the points of the curve in a suitable way.
What you describe in your question, i.e., encode $m$ as $mP$, is also known as exponential ElGamal and typically
used to make it additively homomorphic. But in this case, you have to compute discrete logarithms after decrypting.
Note that decryption will yield $mP$ and you have to compute $m=\log_P mP$ which means you have to solve the elliptic
curve discrete logarithm problem. This is only practical for small messages.
Map Messages to the Curve
A standard probabilistic encoding that can be used for curves over $\mathbb{F}_p$ (for a large prime $p$) is that you fix some value $\ell$,
for instance half the bitlength of $p$, and then simply choose a random integer from $\mathbb{Z}_p$ and set the least
significant bits of this value to represent your message, i.e., you have a value $r\|m$. Then, treat this value $r\|m$ as the $x$ coordinate of a (potential) point on the
curve (in affine coordinates). If it is on the curve, take one of the two possible $y$ values and you have your encoding of the
message to a point. Otherwise, start over again
with a new $x$ value.
This is one probabilistic encoding and if you want to have injective maps that
are also efficiently invertible take a look here as pointed out in my comment.
Third possibility: Avoid ElGamal
As @poncho pointed out, you could simply replace ElGamal with another elliptic curve encryption scheme such as
ECIES. It is a hybrid encryption scheme and avoids
the task of mapping messages to points on the curve. In practice this seems to best solution if you want to use
your scheme simply for encryption (and do not need it as a building block in protocols which require proofs of
knowledge or stuff the like).
