Yes, make the font reasonably sized. If you need to see too much code on the screen it means you've got either a bad design or a poor implementation.
Make sure your lines are of reasonable horizontal length: about 80 characters in a reasonably-size font of a fixed-width typeface is long enough. About a thousand years of research has shown that about 3 inches (7 cm) is about the ideal horizontal line length for readability and the elimination of eye strain when reading the printed word. Your eye are no different. Many coding standards eschew this wisdom in favour of cramming more code on the screen to accommodate the bad design or implementation, at the cost of diminished readability and increased physical and mental strain on behalf of the reader.
Make sure your code has enough vertical whitespace. You will notice when reading printed matter that paragraphs are often separated by a leading of 1 or 1.5 lines. This gives a physical pause between the visual scan of conceptually related ideas, which is not only restful for your eye muscles but aids in readability and understanding of your code. Many coding standards eschew this wisdom in favour of cramming more code on the screen to accommodate the bad design or implementation, at the cost of diminished readability and increased physical and mental strain on behalf of the reader.
As mentioned above, adjust the contrast of your monitor. A typical computer monitor display really really crappy text and you're going to fatigue sooner or later, but a monitor at eye level and the right distance from your face, with appropriate ambient lighting and contrast, can make a dent. Really, the only solution to the crap display problem is to get a nice 24" monitor with 600 dpi minimum. Best of luck with that in the next few decades.
Most of all, programming should not involve long periods of time staring at a crummy display and reading poorly laid-out text. As advised above, take breaks from typing to, for example, design, think, walk, get exercise, eat properly, nap. Also, look up from your monitor at least once an hour and focus on something farther away, like the view out your window or the panel wall on the other side of your parent's finished basement.
These are all bits if wisdom gathered over many years. If you're young, do ignore them and invent your own solution. They'll be there return to when you need something that works.