I do not think the Arduino Uno can handle the power of the (180 mA) pump. The pump works on 3.7 V very well, according to its posted specifications.
The type of battery to use is then limited by:
- Voltage above 3 V - to operate the pump
- weight - the maximum load the drone can carry
Alternatively, a small container may suffice (no pumping).
To debug the code (if the code is the cause of the problem, which I doubt):
- comment each section out of the two (servo and pump), one by one.
- check correct working
- un-comment
There is a command in A IDE to comment-uncomment.
Myself I would not do this check by supplying power directly from the Uno.
Another problem - which I encountered many times - is the lack of the common ground. Check whether there is a correct common ground for all your components. Sometime is not that easy to spot.