Originally Posted by SkyDog75

As counter-intuitive as it may be, fractional tire sizes (16 x 1 3/8") and decimal tire sizes (16 x 1.5") are typically NOT interchangeable. The rims for those sizes are often a few mm different in diameter. Heck, in this case even fractional sizes may not match up because there have been a few different 16" fractional standards. 16 x 1 3/8" tires typically have a bead seat diameter (BSD) of 349 mm, but Sheldon Brown's site mentions two other 16 x 1 3/8" specs plus Schwinn's 16 x 1 3/4" tires that have a BSD of 317 mm.

Since there have been a LOT of different tire sizing systems, some of which are easily confused like the various 16" sizes, the ISO and ETRTO came up with their own sizing system based on consistent measurements instead of arbitrary labels. You can typically find the ISO size on a tire's sidewall even if it has some other sizing designation as well. Do you see any marking like "37-349" on your current 16 x 1 3/8" tires? That designation means the tire is 37 mm in width and has a bead seat diameter of 349 mm. If you find any other tire with a "-349" size and reasonable width, it'll fit your rims.

But to cut to the chase, I don't know of any size with a 349 mm diameter other than 16 x 1 3/8". You may be limited to that specific width.