Injecting IM solution into a blood vessel is excruciating and you and the provider would notice it immediately if it happened. It is likely to cause an embolism and possibly kill you, but I don't think it would be unnoticeable and then cause a thrombus multiple days later.

There are also not a lot of major vessels near common injection sites, for this reason. It's possible and rather common to nick a surface capillary or something, and those can bleed quite a lot, but a vein or artery would be totally different. Swelling, horrible pain, likely a cough.

Source: inject myself with intramuscular estrogen every week.