"that I see only the image on the screen, and not my own reflection, or the neon lamp"
Given your standard of effectiveness, then yes, there are effective anti-glare screens.
Solutions like the 3M Privacy Screens are, as far as I go, grossly over-priced. You may want to trial more generic solutions on Ebay. Just search on Ebay for
Anti-Glare laptop screen Protector to find vendors such as this or that one. They have a wide range of different screen size and aspect ratio combinations, and you should take both factors into account before buying a filter. They're also cheapish, in the 10-15$ range.
I recently got myself a matte filter for my
12.1" laptop (
16:9 aspect ratio) from the first vendor. It's not as matte as I would have liked it to be, but it's definitely an improvement! (It's only slightly less matte than my matte-panel desktop monitor.) Before I was always staring into the reflection of myself all day long; now this reflection is much attenuated, to the point where you can easily forget about it. Well worth the money!
Just make sure to properly clean the monitor before applying the filter (literally remove all dust particles), so as not to get such a botched result:
Other than the air pockets on the top half of the monitor (did I mention the need to remove all dust particles?), notice how the screen with the filter is noticeably less reflective than the surrounding glossy area. Before I applied the filter, the screen itself was more reflective than the surrounding area.