I use contact lenses basically every day, and I have had no problems working in front of screens. There's a huge difference between the different brands. Mine is one of the more expensive ones (Acuvue Oasys 1-Day), so that might be part of it, but each eye is compatible with different lenses.
If I were you I would go to an optometrist and talk about this. They can also often give you free trials for different contacts and you can find one that works for you.
FWIW, that is the same brand that I use and was specifically recommended for dry-eyes by my optometrist. I still wear glasses most of the time because my eyes also get strained from looking at a monitor with contacts in.
I'd recommend a trial of the lenses to see how they work for you before committing to a bigger purchase.
If I were you I would go to an optometrist and talk about this. They can also often give you free trials for different contacts and you can find one that works for you.