There is no rule that all the verbs in a sentence must have the same tense. The tense of each verb should match when the action in that verb occurs. It is perfectly reasonable to mix tenses if that accurately matches when the action occurred.
Perhaps the most obvious example would when you are describing a series of actions. Like, "Yesterday I ate eggs for breakfast, today I am eating pancakes, and tomorrow I will eat cereal."
But it's possible -- and common -- in more complex sentences. Like, "When I was young I thought that someday I will become a millionaire." "Thought" is in past tense because I was doing the thinking in the past. "Will become" is future because I was thinking of an event that will happen in the future.
In your example, "I was feeling the fear rise up ..." "Was feeling" is past continuous, because the feeling occurred in the past but continued over a period of time. "Rise up" is present, because at the time I had the feeling, I was feeling that something was happening in my then-present. In this case, you could also say "rising up". The difference is point of view. If you write "I was feeling the fear rising up", you are saying the rising was in the past, from your point of view now telling the story. If you say "rise up", you are saying the rising was present, from the point of view of the character ("I" in this case) experiencing it at that moment.