Depends on what is going on with the relationship. If you guys have moved in together or started spending more time together; then you are getting to know their quirks and they are bound to do something that irritates you and vice versa. If you are just nit picking at each other about silly things; then that is completely normal! Even screaming and getting made at each other are completely normal. Everyone fights and sometimes you go in patterns where you will fight more often then others. Relationships are hard to make work! And you both have to be willing to make it work or it won't.
Anyhow, my answer is that it depends on what you are arguing about, how bad the fights get, and what changed in your relationship. If they are really bad fights then you should rethink your relationship, but if they are normal fights without violence or signs of violence or any other abuse; your arguments are likely healthy. If something changed in your relationship (Just moved in together, been separated long, lack of sex, spending a lot of time together, or anything along these lines); it's likely just the strain of change. If you are arguing about things that will effect your future or your relationship you should reconsider your relationship.