Is UCC28610 the correct device for the condittion?

The best way to determine if the UCC28610 is suited for your design is to input your specifications into the Design Calculator tool that is available in the tools folder of the UCC28610 product folder (http://www.ti.com/litv/zip/sluc113d).  If the design can satisfy the 1A to 4AA peak primary current, 1.5us to 5us maximum on-time, and switch within 30kHz and 133kHz then the calculator will generate the required comp0onents.  If the design is not suitable, due to the inability to design a power stage that will meet the mentioned requirements, the design calculator will tell you in rather large red letters that this is not an appropriate choice.  Give it a test drive...

I designed the calculator spreadsheet to iterate the inductor value so it does increase it in the attempt to satisfy all of the devices criteria.  I ran your input voltage and output spec through my MathCAD file and unfortunately, due to the low input voltage, I can't get the inductor value to converge on simultaneously meeting the peak current limit of 4A, the maximum on-time of 5us, and the switching frequency without triggering power limit during the normal operating parameters.  The UCC28610 will not work for this application and it is not recommended.  The big red text is there to tell you that it tried really hard but just couldn't get there from here. the UCC28610 is a great device but the internal logic has specific criteria that does limit its use (peak current, frequency, on-time, watts per micro-henry power limit).

 I suggest you look at the UCC28600.  It may be just right for your application.