Oh please don't be too embarrassed at getting off to walk up a hill.
I do this sometimes too. It isn't worth it to me to burst a carotid artery just so I can stay on the bike going up a hill. Sometimes I get off because i am going so slow that i am afraid of falling over!
and SOMETIMES i get off and walk because I don't want to get overheated.
There are lots of reasons. maybe you can train on hills that are just a little hard for you and when they become easier, tackle a bigger hill?