Genealogy /
THE MEANING AND RESEARCH OF MY POLISH LAST NAME, SURNAME? [4500]
The name may be derived from the estate Swiecice
you have an answer in your own question - Święcicki simply means from Święcice or of Święcice - surnames of that type were common for nobility ( a contraction of pan Święcicki in your case (the lord of Święcice)) but were not restricted to nobility (in later times when peasants were given (or adopted) surnames some ended up with surnames of that type) - if you have family records you can probably establish if your family had noble roots
the place name Święcice is not an unusual one and there may be a good couple of places named so in Poland and therefore there could have been several unrelated families bearing the surname (hence the mention of the surname in conection with various coats of arms).
as for Baltic ancestry - hmm I am not sure about it but it is quite probable that the whole north of Masovia has a Baltic genetic substratum (i.e. that there were a significant number of Slavicized Balts living in the area dating back to the migration of Slavs) - another possibility is the flux of genes because of frequent warfare including taking slaves and hostages between Prussians, Yotvingians and Polish Masovians with raids on both sides of the border - another possibility is that some splinter fraction of Prussians or Yotvingians seeked shelter on the Masovian side after the conquest of first Prussia then Yotvingia by the Teutonic knights (they would have been required to adopt christianity in that case)