My bike makes a constant squeak noise
Bicycle drivetrains can make all kinds of squeaking or creaking noises and it's not obvious where exactly the noise is coming from. You have to use a process of elimination to track them down.

Can you replicate the noise with the back wheel off the ground and turning the pedals by hand. If so is the sound coming from the front crank area or the rear derailleur area?  

Does the noise continue when you stop pedaling? If not turn your attention to the rear wheel.

My first guess is that your chain is not lubricated properly. Dry chains tend to squeak. Bad rear derailleur indexing, chain rub on front derailleur tend to clatter or rattle. Bottom brackets tend to creak more when applying high torque through the pedals.

Another prime suspect would be the rear derailleur jockey wheels, but you said you just replaced the derailleur.

Check the crank is spinning freely and there is no play in the bearings. This is easier if you open the front derailleur cage and pop the chain off the chainrings. 

Also check both the pedals are turning freely and there is no play in the bearings. Try unclipping one foot at a time while riding. If the squeak disappears when you unclip a foot it's that pedal.