I am not entirely sure what these bumps are. It is often hard to suggest potential diagnoses for problems like this over the internet without being to examine the spots closely. Therefore, I suggest that you go in to see your primary care doctor
, who will be able to help figure out what is going on.
One possible cause of red bumps are canker sores. These often occur in locations like the one you describe, the inner lip. No one knows exactly what causes canker sores, but they are closely associated in some people with the ingestion of certain foods and with stress. They also tend to be at least a little painful, so if the spots you have are not painful at all, that makes the diagnosis of canker sores less likely.
It is also possible that these represent areas of irritation of the lining of the mouth. For example, you say you notice them when you drink alcohol or eat spicy food; these substances might simply be irritating your mouth. If you refrain from these provoking foods and from alcohol and the symptoms improve I think that is a good sign.
Once again, I suggest that you see your primary care doctor at your earliest convenience for help coming up with a diagnosis.