A serious diagnosis would be a cruel blow to Cox, who was set to make his Test debut last year against New Zealand only to break a thumb in the build-up to the first Test.
"Jordan doesn't seem to have much luck when it comes to England call-ups, but his century here on a testing pitch showed just what a good player he is," former England coach Silverwood said.
"His time will come."
Cox's century against Somerset was his second in the County Championship this season - he also made 82 against Nottinghamshire - but, with wicketkeeper Jamie Smith available again after paternity leave, the right-hander was effectively in England's squad as the spare batter.
Jacob Bethell impressed after being called up for Cox in New Zealand, making fifties in each of the three Tests. He would have kept his place in the squad but is at the Indian Premier League and will not be recalled.
If Cox is ruled out, England will have to decide whether it is worth calling up a replacement.
Durham's 20-year-old opener Ben McKinney is highly-rated but missed his side's Championship match at Hampshire this week with a back spasm.
Somerset's Tom Banton is another who fits England's aggressive mould. He has not made more than 26 in seven innings since beginning the season with an epic 371 against Worcestershire.
Banton's 21-year-old team-mate James Rew scored a fine century to seal the win over Essex on Monday and has been in recent England Lions squads, while Sussex opener Tom Haines is the leading run-scorer in the County Championship this season with 513 runs in four matches, including two centuries.