Well, first of all, most likely you wont get any ester at all with that free amino group. You definitely need to protect the amine (experienced that myself with aminoalcohols: full conversion to amide even if more sterically hindered or benzyl protected)
Second, in my experience, adding additional base helps a lot, I used 1equivalent of DMAP and it worked like a charm.
Third, I dont understand why you are pre-forming the anhydride when you can just mix it all together and stir overnight?
Try other solvents, I never used DMF for this reaction but DCM or acetonitrile worked well for me. Especially acetonitrile since you can quench the DCC with oxalic acid afterwards which is more difficult to do in DCM.
Anyway, my conditions that I used for esterifications or amidations:
a) acid (1eq) and aclohol (1 eq) were dissolved in solvent (DCM or ACN), DMAP (1eq) was added followed by DCC (1eq). Stirred overnight at RT, quench with oxalic acid (if in ACN) filter, extract, collumn
b) acid (1 eq) and amine (1eq) dissolved in DMF. HOBt (2 eq) was added, followed by EDCl (2eq). Stirred until completion (aprox. 2hrs), diluted with EtOAc, extracted with K2CO3 and HCl. Purify if needed by column