You have a very good GPA compared to many. However, "competitive" is a relative word. It all depends on supply/demand that school is experiencing. Typically, community colleges and state universities are the most "competitive" to get in because they have the most affordable tuitions. These institutions then have to come up with a set of rules and parameters to select the best students from the pool of applicants they have. Privates schools are easier to get in, but they are also VERY expensive. Whichever route you decide to go, ensure the institution is accredited by the proper agencies.
If you are going for the Associates degree in Nursing, look for NLNAC Accredited Nursing Programs
There is another well known agency, but its name escapes me right now. Maybe someone else can post it, or if I find it... I'll do another post.
Hope that helps!