I think I broke my big toe yesterday, but today the swelling is down some. Should I see a doctor?

Yes, if..... If you think it is broken then you should see the doctor.
Not yet. If it isn't out of place, and you are able to walk around with less and less pain, it's ok to give it some time. Usually we give anti-inflammatory medication, tape it to the toe next to it to give support. Otherwise there is not much needed. If it gets worse or doesn't improve within 2 weeks, go ahead and get it checked out.
Bruising & swelling. Usually with a break, there is bleeding from the bone which leads to swelling and bruising to the toe and surrounding area. This is not always the case, but when i see this, i always take an x-ray to see. There is some degree of pain when the toe is moved at the site of the injury.