I am writing a fiction. I start in first person(I) and then because I had to describe emotions of other characters simultaneously I switched to third person, (referring as she, they or the name of character). The story keeps switching in first and third person so that the reader can get the personal view of different character. Is it acceptable?
Anything is acceptable if you make it work. For an example of a book that makes this work (brilliantly) see Cormac McCarthy's No Country for Old Men.
But any change in narrative style calls attention to itself and therefore has to be handled with care and skill. It may be more acceptable to the reader of a literary novel like No Country for Old Men than of a genre fantasy or romance, for instance, where the reader is often just in it for the yarn and is not interested in, or appreciative of, literary effects.
In other words, if you are doing it because you are a beginner struggling with narrative technique, it likely is not going to work and you would be better advised to pick one narrative method and stick to it. If you are a skilled author experimenting with different narrative methods to achieve a literary effect, you may be able to pull it off.
We should also note that even in books that are ostensibly told from a first-person stream of consciousness point of view, the author can get away occasionally with telling us things about how other characters think or feel that would not be obvious to the narrator character in the moment. Jack Kerouac does this several times in On the Road. This is not necessarily jarring to the reader if it supplies information that is necessary or appropriate in the moment.
Also, don't feel that you have to comply with the current fashion for first person narrative. It is faddish among writers at the moment, but difficult and limiting. Third person is the natural narrative voice of the world's literature. If you are uncomfortable in the straightjacket of first person, write in third.