Bad habits are hard to break, especially those that start in childhood. Blowing your nose can always be disadvantageous to your health. Our hands cannot as clean as doctors. Bacteria and germs are full of them though you may wash them just a few minutes again. Blowing nose is a cause of getting eye infection, especially during your cold. Such behavior just help with virtues spreading. So get rid of your bad habit to keep eye health.
Blowing nose would definitely increase the intraocular pressure temporarily. There is other possible damages need your attention too. We know that the nasal passage is connected with eyes through the internal duct. When we catch a cold, there is always secretion in nasal passage which contains dusts, bacteria and virus. When we blow our nose hard, this secretion might be forced by the air to go up through sinus even back into eyes. This is why people always complain some stuff coming out through the corner of eyes when they blow noses ( tear duct is located in the corner of the eye and it is connected with sinus). This secretion might spread the infection to sinus and eyes, resulted in sinusitis and conjunctivitis. It is better not to blow your nose. If you really need to do it, then do it gently.
Yes, blowing your nose will cause damages to your eyes because of the interlinked nerves between nose and eyes. You'd better not blow your nose often which could also cause the damage of the eyes nerves. You should protect the weak parts of the eyes which are the very important ones in the whole body. If you feel not comfortable at the eyes, you could use the eyes drops and warm compress to make your eyes feel comfortable.
As far as i could know, blowing nose won't causes damages on eyes. And i often do that, and i feel OK in my eyes. But to know more about it. I just make a deep search in google and find the answer. I saw somebody say that it can raise pressure in your head slightly for a quick moment if you blow your nose too hard. If so, it may further cause burst blood vessel in your eye. It sounds really crazy. Maybe you shall consult an eye doctor. Anyway, for the sake of your eyes, you'd better not blow your eyes any more.