A normal Chinese dictionary makes explanations mostly for content words and the use of fairly flexible function words (e.g. 上， 了， 下，过etc.) are usually not included. This is because they are so flexible and subtle that it's hard to get them without enough practices in context. I'm not going into the grammar too much, but if you want to have a better understanding of Chinese through a bird view, it's really necessary to get a general impression of the grammar in Chinese. Like other grammatical function words, 了，来，过，去，'上了' here is a kind of auxiliary-verb-like word, which usually follow an action verb to show tense, state, movement or direction. ’上‘ has several functions as an auxiliary verb. In your example its function is to show the state of attachment or the movement from one thing to another—— Your love has attached to him. Additional example: 请把门关上。 Here '上' also means the state of attachment. i.e. The door has attached to the doorframe. Or the door has changed its state from being open to being closed. '了' is a frequently used auxiliary word to show tense —— start to happen or already happened.

上了here means a new state which might be much different from before. A new state, as a result. You could translate it (上了) into "already". The meaning of the second part of the sentence is: I have been in love with him, or, I start to love him already. Another example:他关上了门。The meaning is: He closed the door, another meaning is that, As a result, the door has been closed by him, before he did that, the door was open.

@Alice thanks!

I didn't know those ones, thanks a lot!!!

我上了厕所= I went to the restroom 他上了车=He got on the bus 他爱上了她=He has been falling love with her 他上了她...=slang ,he has made love with her....