Rand Paul is wrong. What Trump did is distinctly NOT

More than 125 times in our history, Presidents (including in recent times Reagan, Clinton, Bush, Obama and Trump) have taken military actions without the approval of Congress. 

Obama is an interesting case in point.  He sought approval from Congress to launch attacks in Libya, failed to get it and then launched the attacks anyway, arguing that he had the Constitutional and legal authority to do so (which he did).  Two years later, after the chemical attacks in Syria, Obama's "red line" was crossed and yet on that occasion he did nothing, abdicating his own responsibilities to Congress - which he knew would not act.  

Very odd to put those decisions in juxtaposition and try to come up with the reasoning.

In any case, the sort of limited, precise actions such as Trump took do not by any stretch of the imagination rise to the level of "war" as confirmed by repeated decisions of the Supreme Court, and are authorized by specific acts of Congress.  Indeed, such actions are usually taken to interrupt or interdict situations that might, if unchecked, lead to war and/or which directly endanger Americans and American interests, such as the many American personnel who are in country in Syria.  These are situations that require immediate response, not the lengthy deliberative process of "declaring war." 

It's very superficial thinking to equate ANY use of military foce with "declaring war."

Senator Paul might know something about healthcare, but he seems to know very little about the Constitution or the law.  He is an avowed isolationist who wouldn't shoot down a Russian bomber flying over DC until it actually dropped bombs on the White House, and you must never make the mistake of listening to misguided people of his sort - or those of another sort who would criticize a particular President no matter what for purely political reasons. 

Think for yourself.  Get facts.  Knowledge is the best defense against foolishness.