Thanks for your input.
The estimated HLA type from the software shows my sample is heterozygous E01:03:01:01/E01:01:01:01. I subset the reads matching E*01:03:01:01 by samtools view -h input.bam HLA:HLA00936 > HLA00936.bam and then used MUSCLE to align those sequences against the nuclear coding sequences of HLA-E alleles, as you suggested: http://www.ebi.ac.uk/Tools/services/web/toolresult.ebi?jobId=muscle-I20170309-184416-0547-98835251-pg&analysis=alignments.
I also aligned the sequences from the bam against E*01:03:01:01 fasta: http://www.ebi.ac.uk/Tools/services/web/toolresult.ebi?jobId=muscle-I20170309-185005-0383-51440835-pg&analysis=alignments. Do you have any input as to how to retrieve the unique sequences? I'm not exactly sure how the algorithm is making the allele calls, but the developer has stated that the read alignment between similar HLA alleles needs to be optimized.