Listen to Townes Van Zandt, Bob Dylan, Ronnie Drew, Leonard Cohen and some others besides who can put over a song without a lot of range and study how some of these people finesse a note, sing around a note without actually hitting it and manage somehow against all odds and logic.

Know that some of the most influential singers like Billie Holliday and Louis Armstrong really had very little range.

Find songs that fit you that you liked. You master those few that fit you now and you can, after you gain confidence, and you will find out that when you gain your confidence that you can add more songs, including ones you thought you'd never be able to do at first. Just start with the easy and comfortable and the rest will come.