Does the universe ever end? I have meditated and come to the conclusion that the world never ends, that conciousness goes on infinitely. This was ok when I felt I had free will, when I believed I was helping other people, when I thought that even what was apparently nonsense had purpose and when I felt like I could at least to some degree affect the feelings I have and those of others; to make things better for everyone.

But sometimes I feel like I can't, like everything is predestined and there's no control over anything. Like we're all trapped in a giant hamster wheel that runs around and around forever with no exit.

What is the correct way to view this problem?

(Also, you probably need an 'eternal return' tag.)
There were fourteen questions to which Buddha remained silent. The universe is eternal,  The universe is not eternal.. were two of them. Read the following sutta.
MN 63 - Cula-Malunkyovada Sutta: The Shorter Instructions to Malunkya
One day a man called Malunkyaputta approached the Buddha and demanded that He explain these questions to him. He even threatened to cease to be His follow if the Buddha's answer was not satisfactory. The Buddha calmly retorted that it was of no consequence to Him whether or not Malunkyaputta followed Him, because the Truth did not need anyone's support. Then the Buddha said that He would not go into a discussion of the origin of the Universe, whether it is eternal or not eternal etc. To Him, gaining knowledge about such matters was a waste of time because a man's task was to liberate himself from the present, not the past or the future. To illustrate this, the Enlightened One related the parable of a man who was shot by a poisoned arrow. This foolish man refused to have the arrow removed until he found out all about the person who shot the arrow. By the time his attendants discovered these unnecessary details, the man was dead. Similarly, our immediate task is to attain Nibbana, not to worry about our beginnings.
Another Sutta to read in this context is AN 4.45  -  Rohitassa Sutta: To Rohitassa

Once I was a seer named Rohitassa, a student of Bhoja, a powerful skywalker. My speed was as fast as that of a strong archer—well trained, a practiced hand, a practiced sharpshooter—shooting a light arrow across the shadow of a palmyra tree. My stride stretched as far as the east sea is from the west. To me, endowed with such speed, such a stride, there came the desire: ‘I will go traveling to the end of the cosmos.’ I—with a one-hundred year life, a one-hundred year span—spent one hundred years traveling—apart from the time spent on eating, drinking, chewing &amp; tasting, urinating &amp; defecating, and sleeping to fight off weariness—but without reaching the end of the cosmos I died along the way. So … ‘I tell you, friend, that it isn’t possible by traveling to know or see or reach a far end of the cosmos where one doesn’t take birth, age, die, pass away, or reappear.’”
[When this was said, the Blessed One responded:] &quot;In this very one-fathom long body along with its perceptions and thoughts, do I proclaim the world, the origin of the world, the cessation of the world, and the path leading to the cessation of the world.&quot;
When the Buddha uses the term “world” or “cosmos” (loka), his primary meaning is the cosmos as experienced in terms of the six senses. As with the other factors of dependent co-arising, there is no need to study the cosmos “out there” behind our experience of the senses. It is enough simply to understand the cosmos as directly experienced for that experience to be brought to an end.