Keep in mind that patterns and coincidences are an expected feature of randomness. You've stated this very well when you say it "feels" like nothing is random. The human brain has a tendency to assign agency to the patterns it perceives. IOW, our minds aren't happy to simply notice patterns, they also want to think that something intelligent is behind them, and this notion occurs without conscious thought. That's because evolution has primed us to be this way.
There are two types of errors which can be made when it comes to pattern recognition. We can notice patterns that aren't really there, known as a type one error. Or, we can fail to notice patterns that are really there, known as a type two error. Evolutionary speaking, it's less costly to make a type one error. If we notice a rustling in the grass and assume it's a tiger, we run away. If it were just the wind, and not a tiger, so what? The mistake hasn't cost us anything. If we notice a rustling and fail to recognize that it might be a tiger, the mistake can cost us our lives. So, we have evolved to favor type one errors, meaning our brains instinctively err on the side of caution.
At the same time, our brains have not had much pressure to evolve an instinctive understanding of probability and statistics, which means we tend to over or under estimate the likelihood of events and coincidences, and misunderstand the nature of randomness.
"Not understanding just how much of your life is governed by randomness generates many a fallacious belief about the way that the world works. It should be clearly understood that randomness creates coincidence. That is to say, if there were no coincidences in life, we could speculate that some outside force is controlling the events in our lives. However, with true randomness comes the expectation that coincidences will happen: there will be cancer clusters, your friend will call you just when you were thinking about them, and last night’s dream will have somehow 'predicted' the events of the following day." - Kyle Hill