Did you regrind the plates and are the new shoes the same type? Replacing the shoes only means they have to wear a bit to fit the grooves in the old plates. Give it time. Also rebleed the brake cyclinders and get rid of that contaminated fluid.
If you only did the front brakes, the problem may be in the rear brakes.
All cars have the brake system designed to make a loud screeching noise when the pads get low. Most people do not do the proper maintenance on their brakes, which is lubing of parts. This maintenance ensures even wear of the pads and or any problems will be noticed. Most braking is done with the front brakes so rear brakes tend to last much longer. Five plus years before having to do the rear brakes is not unusual.
Were the rotors resurfaced or replaced, or just the pads? Warped rotors are the most common cause of vibration when braking
New fluid will be in system almost immediately but if you need to bleed system brakes will not perform properly until they have been bled.
You can tell if a Lincoln needs a new rotors by the braking fashion of the car. When applying the foot to the brakes, if the pedal tends to vibrate, the rotors could be deteriorating.
You need new brakes
It depends on the vehicle and how hard you'll be braking! Basically drum brakes are quite old fashioned and can 'lock' under hard braking or if they get wet. This can cause the wheel in question to skid! Most new vehicles these days unless they are very cheap (usually motorbikes) come with disk brakes. They won't lock if they get wet or under hard braking. Also disk brakes can have an extra feature called ABS - or Anti-lock Braking System - what this means is that when you press the brake pedal the brakes automatically turn on and off a hundred times a second or so - actually allowing you to steer. Very good. Nearly all cars and many motorbikes come with this feature as standard or an option.
Even if you have brand new or good brakes when the pads become hot from braking and then cooled very fast from water then the pads tend to crystalize creating the squeaking noise when you brake you just have to let them squeak it out
have the back brakes checked sometimes they can sound like the front
That is strictly a function of your driving style and the type of driving. Brake pads can wear as fast as ten thousand miles or last even longer than one hundred thousand miles, depending on how often and how hard the brake pedal is pressed. If the brakes are used so often that they overheat, or if the driver "rides" the brake pedal, the rotors will warp, resulting in a pulsing sensation when you use moderate braking. In any case, brakes are generally quite durable, but drivers are quite unpredictable.
carbon ceramic brakes are fade-free, which means they will last much longer than conventional brakes
Follow the brake connection bar under the frame to the brake system. Get someone to put the brakes on and off while you learn how they make a braking action.There should be an adjustment nut to tighten the pressure. you may even need new brake pads.