Synthesis of Aspirin, made unknown fluid
Often, acetylizations are performed with acetic anhydride being deployed both as reagent, as well as solvent.  Consequently, acetic anhydride is used in excess when referring to the number of $\ce{-OH}$ to react.

The addition of water you describe in step 3) intends to hydrolyse this excess of acetic anhydride to form acetic acid.  Apart from acetic acid equally representing a good solvent for many organic products, it takes time to complete this hydrolysis of acetic anhydride. You may accelerate the hydrolysis of the acetic anhydride if the beaker is immersed into an ultrasound bath, or just continue stirring the mixture at room temperature as usual.

The second point is, albeit its high melting point (136 $\mathrm{^\circ{}C}$), the crystallization of aspirine equally takes some time, too. Crystallization of organic materials from water may demand some more attempts prior to success than from organic solvents, too.  Cooling the mixture often will lower the solubility of your product in the solvent, however, if cooled too quickly to too low temperatures you may obtain either just a glassy gel / syrup instead of a solid easy to filter off, or a solid that has to be recrystallized to purify it further.  Scratching the inner walls of the beaker with a glass rod intends to create fresh sites where crystallization may start.

For peracetylating glucose with acetic acid, for example, it is not too strange to stirr the quenched reaction mixture with an excess of water over night at room temperature to convert the initially "honey-like" product into a good solid.