I know that when an object A does positive work on another object B, object A loses energy and object B gains energy(there is transfer of energy from object A to object B) and when object A does negative work on object B, it gains energy and object B loses energy(there is transfer of energy from object B to object A).
Now, when we lift an object(standing on the Earth), we do positive work on the object and so the energy of the object should increase (and our energy should decrease) while the Earth by its gravitational force does negative work on the object and so the energy of the object should decrease(and the energy of the Earth should increase).
Now my question is, is the energy of the object increasing or decreasing since it cannot be both at the same time.

The Work-Energy Principle states that the sum of work done by all external forces acting on a body equals the body's change in kinetic energy. In the case of lifting an object, work is done on the object by the person lifting it and negative work is done by gravity as the object rises. If we assume for a moment that the magnitude of the lifting force is equal to the gravitational force (i.e. its weight), then the sum of work done on the object by the lifter plus work done by gravity is zero, and kinetic energy and velocity of the object remains constant throughout the lift. The important point is that the total work done on the object is zero. But wait - doesn't it gain potential energy as it rises? And if so, doesn't that mean that work must have been done on it? Yes, it does - the change in gravitational potential energy of the object is the negative of the work done by gravity on it during the lift; it has nothing to do with the work done by the person lifting it. The mathematical calculation of delta PE is:

\Delta PE = \int _{R_1} ^{R_2} \frac {GMm} {r^2} dr = GMm(\frac 1 {R1} - \frac 1 {R2} )

which for objects in a uniform gravitational field (e.g. near the Earth's surface) is simply:

\Delta PE = mgh

This I think gets to the point of confusion - when you perform work on an object by lifting it you may have an impact on its KE, but any change in PE is directly due to the negative of the work done by gravity, not the work done by you. Hope this helps!