Could getting strangling while bulging your eyes cause problems?

Yes. Yes, generally you should close your eyes while being strangled (sorry). This is a very unusual question. Extreme straining of the eyes (valsalva) can cause problems. Severe macular hemorrhages have been reported, as well as optic nerve and even vitreous hemorrhage (usually trauma related - Purtscher's retinopathy). People with shallow orbits (not deep set) can be at risk for globe subluxation too.
Neither is good for . Eye pressure. Would not advise either strangulation to cause bulging of eyes. Anytime you cut off circulation at such a high pressure, you can cause tremendous damage to the retinal circulation of your eyeballs. Would advise against being in such a situation at any time. Not worth it in the short or long term.