Don't beat yourself up about this, Lily, mortgage rates have been low for so long, most people (me included) didn't think about payments going up significantly. You've just been unlucky in the timing of it, and in having a shitty government who don't really care about average homeowners.
I agree with the others who say that you should take your parents up on their kind offer, they want to help so let them. That will give you some breathing space and let you see what your new rate will be, as well see how energy bills go. You mentioned a pay rise which may be small but it all helps, and also you may have extra theatre shifts by then. See where all that leaves you before thinking about another job, you'll wear yourself out.