I am 19 years old and a last baby tooth fell out today. Will my teeth move into the open space and straighten out?

No. If you are 19'and your last baby tooth fell out, you are probably missing a permanent tooth that would have erupted under it from birth. Go to your dentist and make sure that tooth is missing. Teeth do not move sideways to occupy a lost tooth space. They collapse, which ruins the total bite if you do not fill that space one of three ways; a bridge, a partial, or an implant . See your dentist.
Check with a dentist. You do not mention what tooth fell out, sometimes with the permanent tooth that comes in, it will fill the gap. However if your teeth seem out of alignment to begin with youogjt need to check with an orthodontist, to see if you might need braces.
Absolutely not. If you had baby tooth 'till now, is underlying permanent tooth missing or impacted? If space is not controlled your other posterior teeth will literally collapse into the space. Crooked front teeth will not magically straighten. Please see an orthodontic specialist now before a complex malocclusion becomes a dental disaster. Easier, faster, cheaper to fix now than in the future.