If you are 2-3 weeks pregnant, a pregnancy test would be positive if you were pregnant. Pregnancy tests pick up your hormone levels 10-14 days after conception, which is generally about the time of your missed period.
The pregnancy symptoms while nursing are going to be the same pregnancy symptoms when not nursing. Since your son is almost 2, I'd imagine he is nursing for comfort a few times a day but not a lot since he is eating more solid foods now.
It sounds like you might just be run down.
Another thing I'd like to address, pregnancy symptoms are not indicative of pregnancy. You are more likely going to get a missed period and positive test before your real symptoms start. This is because the same hormones that trigger pregnancy tests are the hormones that cause symptoms. Negative test = what you are experiencing is not related to pregnancy. That does not mean you aren't pregnant for sure, but it means your symptoms aren't pregnancy related.
Good luck!