is こちら and 私 interchangeable when using を after ?
To directly answer this question, yes, and no. It is not a one to one conversion. The reason for this relies solely on the difference between the words.
こちら: The dictionary definition of this word is varied and diverse. The definitions you will encounter are,
this way/direction; here; this (one); I; we; me; us; this person.
The thing about こちら is that you have a sense of vagueness about the subject you are talking about. So when you say
こちらを見ていた, you could reasonably linearly translate that as,
Me (object) looked at, or
This way (object) looked at. Typically though, the vagueness of the word eliminates
me as an option, because it is not directly clear what/who you are talking about.
The vagueness is intentional for two reasons. First, Japanese people don't like to be direct when they are referring to themselves in a humble way. It comes off presumptuous to assume she was looking at me, when she could have been looking elsewhere. It (very slightly) elevates her in the communication, and distinguishes her as a person that is respected by the speaker.
Second, it is altogether plausible that she wasn't looking directly at you, but at something behind you/to your side, so looking 'this way' could technically be more accurate than 'at me.' Unless she confirms what she was looking at, we just don't have any way of knowing for sure.
Replace こちら with 私, and you start making strong assumptions at exactly what she was looking at. You also remove the sense of respect (however small) that you would have had in the other sentence.
In practice, the difference between こちら and 私 in these sentences is the same the difference between,
looking this way and
looking at me, as noted in the comments by @user4092.