Soldering Inhalation problems?
Since you don't breath with your stomach, there's no way for solder fumes to have gotten into your burps. So, you smell something, but it's not the soldering.

Generally, you should solder with sufficient ventilation. 

On the short term, solder vapors can lead to headaches, on long term exposure, especially lead solders can lead to toxic accumulation effects. We're talking about months of exposure here, not 15 minutes.

So, nothing bad has happened to you, and likely ever will, due to occassional soldering. Again, do make sure next time your workplace is well-ventilated, and you don't need to worry. Try not to hang your head into the smoke; that way, you don't risk breathing in much of the fumes.

Now, I don't want to play down the risks: hypersensitivity to the smoke that colophonium (still the main component of solder flux, i.e. the thing that smokes the most when you solder) and even asthma are relatively common things that you see in people that have been soldering for a living for many years. Again, the dosage of irritating/toxic fumes that you can get in 15 minutes is very likely completely negligible. 

So, a 30min stroll along a somewhat busy road is probably much, much worse for your health than your soldering experiment. You probably really got a small headache, and I can fully understand that worries you. As said, try not to hang your head into the smoke next time, and solder so that the fumes directly leave the room e.g. through a window.

If you plan to solder more often, you can consider getting one of these small solder fume "suckers" (correct name is probably something like "spot suction system", like an air filter that sucks in the air close to your soldering iron).