This is a participle. It cannot be a gerund, because gerunds have a nominal or adjectival meaning (for example, Swimming is fun - swimming would be a gerund). The -ing form itself is not a 'verb phrase', but 'sneezing uncontrollably' is. So if we are looking only at 'sneezing', the answer is 'participle'.
This line is foreshadowing because it implies that anything -- even people -- that becomes a burden can easily be destroyed.
Later, when Beatty himself becomes a problem, Montag burns Beatty to death. When Montag killed Beatty, he destroyed the responsibility he owed him. In this way, this line is an element of foreshadowing.
The word part com means, towards
