Unless you enclose the drip chamber in a lightproof box, which is not really appropriate as the drips must be visible to others, you need to use modulated light - whether it is visible or infra-red - so that the sensor does not respond to illumination by ambient light.
The second problem is alignment. You may need to allow for the drip chamber not to be precisely vertical so the drops do not fall down the centre. Also, a drop is of course, transparent, and as it obstructs the light beam, it does not do so completely, so you are looking for a decrease in the light but not complete blocking. An interesting alternative is to detect scatter instead - have a black pad opposite the light source whether laser or not, and sense perpendicularly to the beam. Again, modulated.
You may not realise this, but while optical drip sensors were used at one time for this purpose, they proved to be quite unreliable and have therefor been completely replaced by peristaltic pumps.