You could. That’s an option. There are also a few schools in between Ivies and good publics with engineering. You may want to consider those as well.
You have a lot to offer. Many schools will want you as part of their class.
What is your home state?
Are you male or female? (That can make a difference sometimes as some schools are all women and some have too many women and need men.)
You may want to look at Union College in Schenectady NY. They have engineering in a small liberal arts setting. Your GPA is on target for Union and they provide 100% of determined need (that doesn’t mean you will go to school for free but usually it means that it will cost you what you can afford. Sometimes that means it’s cheaper than a state school) http://www.collegedata.com/cs/data/college/college_pg01_tmpl.jhtml?schoolId=157
Here is the college’s website-- https://www.union.edu/
Before I try to list other schools, it’s probably good to know what your home state is and what region you might want to attend school in.
You may want to look at Cornell CALS majors because there might be something there that you like. for CALS you need to apply directly to the major. Cornell is also amenable to CC students transferring in. https://admissions.cals.cornell.edu/academics/majors