I don't think they need to be put through that all the time.
Soap works. Add a little bleach or a little vinegar to each wash load. That will sanitize them.
As for drying them you just put them on medium setting and they come out fine.
If your allergies are so bad that you can't use your sheets without them being almost boiled every wash load then you might want to consider buying white sheet fabric and prewash it on the hottest water possible and dry it extended amounts of time on the highest heat setting on the dryer then make a set of sheets to fit your bed.
The white cotton won't fade or get bleach spots or be ruined by chemicals to clean them.
If you make them AFTER they've been washed and dryed on hot hot hot water and super high heat then they won't shrink anymore.
Otherwise, if you're going to continue to wash your sheets on a sanitize cycle that lasts for 2 hours in super heated water then in the dryer on the hottest temperature for a longer time you are going to wear them out and shrink them horribly. But the next size up or make your own.