Maybe use a USB mouse? I do not use touchpads, I stick to a mouse.
I did read a couple of years or so back when I was looking for a new monitor about some screens having flickering backlights and some being flicker free.
Pulse
Width
Modulation is often used to control the backlight when it is not at 100% brightness. This can cause some people big problems.
An in depth article about PWM
A little easier article about PWM on notebooks
Avoid white screens which are littered all over the internet because people think white screens are the same as white paper. Use browser extensions which replace the background with more eye friendly colours. Opera, Firefox and Chrome have these extensions but one for Firefox is best IMO. Dark Background and Light Text v0.5.14 is best of all in my experience because it also replaces Mozilla website backgrounds and also the Firefox Addons page background too. Yeah no white backgrounds!
Could you not get the screen fixed? Would that work out cheaper? Is it a laptop? You have not indicated what type of computer you are looking for.
I use a combination of browser extensions (Dark Background and Light Text) and f.lux (freeware) to lower my display brightness. This might not work well on displays that use PWM but it works well on my display with no issues for me. Alt and Page-Down lowers the screen brightness. It is meant to adjust the brightness throughout the day 6500K during the day and reducing to a low level at night. This is meant to help reduce disruption of the body clock.
Ideally you would avoid buying a new computer ATM because Intel and AMD are attempting to fix the security flaws that have been found in their CPU's. All current CPU's are affected and the software fixes slow down computers.
Does you computer/laptop etc have a monitor output? Could you buy a new monitor and use that? If you could see one before purchase that would be best, otherwise use Amazon, ask questions and read reviews.
Look at monitor review sites to find flicker free and eye friendly monitors:
http://www.tftcentral.co.uk/reviews.htm
Some of the screens look on the large size
https://pcmonitors.info/
Be aware of the maximum output frequency of you computer because it might not be able to match the speed of some monitors. My Intel graphics cannot match my monitors maximum refresh rate 144Hz, it can only get to 120Hz. You might have to use it at a lower frequency, maybe 60Hz. Check your computers output connections too and make sure that they match the display.
There are some different aspect ratios too. Many are 16:9 but some use 16:10, others are extra wide screen.
There are IPS, VA and TN panels and each has it's positive and negative points. IPS better colours but with IPS glow, VA great contrast but poor transitions on some colours. TN has poorer colours but fast refresh rates and pixel responses ie less blurring which is something I dislike. I did try a VA panel and really disliked it because it had terrible blurring when scrolling webpages. White backgrounds are less of a problem but I dislike using white backgrounds.