Am I allowed to throw a bridal shower during the Omer period?
It is permitted, provided that there is no music, dancing, and so on.
Sources: A bridal shower is a gathering of the bride’s friends, which is generally intended for giving the bride gifts in advance of her wedding. In itself, such a gathering is not prohibited in the Omer period, just as one can have ‘birthday parties’ and the like during the omer time. However, one would have to ensure that the event does not deviate from principles of the Omer (music, dancing). See Shulchan Aruch 493:1, Be’er Heitev 2, Mishnah Berurah 3.