So I have been using bleach for quite a while to hide them but I have recently noticed that my skin is getting all red & then brown coz of that. May be its coz of the burning sensation I get. Is there anything else one can do to hide them without doing threading? 
Re: Fine Hair
I'd suggest to invest in a laser treatment home kit. I'm gonna buy one for myself after Eid.
Re: Fine Hair
^ But they are expensive too. Which brand you will go for?
Re: Fine Hair
Could be the ratio was off, and you added too much activator, or the bleach has gone too old.
The darkness should go away in a couple days. To help it along use any sort of natural bleaching agent (lemon juice, cucumber, yogurt + gram flour, etc) on the area, and use sunscreen when going out to protect from further darkening. The little bumps will go away too, but you can use witch hazel to help them along.
You mentioned you don't want to thread, so I'm assuming you won't want to wax either. Have you heard of no!no!? Its an electronic device that burns the hair. An at home laser system is another option as hareem01 mentioned.
Re: Fine Hair
Try sugaring . Its less painful than threading and waxing as you can remove a large area in one go. Another option is using depilatory cream made specially for the face. Or if its fine just leave it if it doesn't show.