The answer above regards your first question having to do with taking Benadryl for allergies. This will give you more information regarding Benadryl and pregnancy
Benadryl would probably safe during this last part of your pregnancy, as far as your baby is concerned, but you should definitely clear this with your obstetrician before using the drug. You should also ask for suggestions regarding other non-sedating antihistamines. Benadryl is definitely contraindicated while breast feeding.
The risk to you and the baby is that this drug can make one drowsy and problems could arise for both of you in a number of circumstances such as driving, walking down stair etc.
Assuming there is no personal contraindication (such as a previous adverse reaction to Benadryl) you probably could take it for allergies that involve your nose (allergic rhinitis). However, you would be well advised to take one of the more recent generation of antihistamines, most of which avoid the problem of drowsiness and a number of which are available over-the-counter. If you have any doubt about which to take, give your doctor or his nurse a call and ask which of these they would recommend.