I think you are asking the wrong question. You should be fine applying to law school if you graduated from "undergrad" early, but I suggest talking to the patent attorneys from your internship about your plans.
Odds are that these guys were doing patent
prosecution (i.e., dealing with inventors, writing new patents, and working with the patent office), as opposed to patent transactions or patent litigation. This is a
very different career path than the average lawyer, and there are a couple things you should know.
First, prosecution requires you to get registered with the USPTO. You can learn more about registration
here, and the general bulletin with the requirements can be found
here. You don't have the right kind of undergraduate degree, but you can still take the exam if you have taken an equivalent number of classes in the hard sciences. You can check out the bulletin and read the fine print, but the gist is that you need to satisfy one of the following:
i. Option 1: 24 semester hours in physics. Only physics courses for physics majors will be accepted.
ii.Option 2: 32 semester hours in a combination consisting of the following: 8 semester hours of chemistry or 8 semester hours of physics, and 24 semester hours in biology, botany, microbiology, or molecular biology.
...
iii. Option 3: 30 semester hours in chemistry. Only chemistry courses for chemistry majors will be accepted.
iv. Option 4: 40 semester hours in a combination consisting of the following: 8 semester hours of chemistry or 8 semester hours of physics, and 32 semester hours of chemistry, physics, biology, botany, microbiology, molecular biology, or engineering. (For Computer Science, see other acceptable course work.)
Second, many patent prosecutors work for a law firm before going to law school. They usually start as a patent agent or some kind of "technical specialist/advisor" (basically a patent agent in training). These jobs give you a taste for what the work is like, and many of these firms will
pay for your school if you agree to continue working part time. This can change the financial calculus about attending school, and its a niche area of the law where the normal assumptions about school rankings, working in big-law, long-term career prospects, etc., don't always hold.