Light is not infinite. Light does not travel infinite distances either - it can, as far as special relativity is concerned, but general relativity combined with astronomy indicates that the universe is expanding and that light will eventually be unable to reach objects that are too far away because of said expansion.

Light can go an infinite distance, as long as it doesn't hit anything that absorbs it. Light isn't infinite - light comes from sources, and the light stops when the source is turned off.

Our sun, for example, will run out of fuel after it burns for about 11 billion years. Nothing, and no one, will travel through space forever. Moving takes energy, and the energy eventually gets used up. Sun Lifetime.
Light traveling.

Whether we describe light as infinite depends strongly on how we define the word "infinite". There are some commonly accepted definitions of "infinite" in science, such as "without boundaries", but being in motion forever is certainly not a sufficient definition. If we look at Newton's First Law, we read that "an object in motion will stay in motion until..." while also knowing that objects referred to in this law are typically not what we would describe as "infinite".

An object (or person) traveling with nothing to stop it (him/her/them) is not therefore infinite, at least not by the sole criterion of "traveling infinitely". If we bring the concept of infinity to humans, and suppose that a person lived forever, that would still not make this person infinite, because we did not touch on the idea of infinity with regards to other aspects of this person. For example, is he infinitely strong? Is he infinitely intelligent? And how would we measure whether he is infinitely "something" or not? If he can lift the heaviest object in the universe, can we call him infinitely strong? What about other universes or potential modes of existence? I think we can see that the question quickly escapes the realm of empirical science, and instead becomes very philosophical.

As for the concept of infinity with regards to light, we can see that light may travel infinitely in space as long as it does not encounter objects with which it can interact, but we already said that this characteristic alone does not make light infinite. The idea of infinity is certainly an interesting one and worth thinking about, but whether an infinite entity exists that we can see, understand, or measure in the ways we think we should observe, study, or estimate is very much unknown.