Talk to your OB GYN regarding any early testing to make sure everything is okay with your pregnancy. My wife had several issues that finally worked themselves out with early detection of issues and testing. That is why we have a 2 year old and an 11 year old :)
"Side effects" of hypothyroid meds, are those of hyperthyroidism. Make sure you start out at a very low dosage (12.5-25 mcg/day) and work your way up, in order to prevent reactions from the med.
Although 6.78 is abit above range, it's not drastically high. You were able to conceive so that's a good thing. I would recommend that you monitor ur levels and also post them here. Med's for hypothyroidism will take several weeks to take affect, although you may develop side effects before hand.
Levothyroxine takes approximately 6 weeks to reach full potential in the blood. While your TSH is over range, it's the FT3 and FT4 levels that are the most important, since TSH is a pituitary hormone and can vary for a multitude of reasons, even intraday.
When you get the results for the FT3 and FT4, please post them here, along with the reference ranges, which vary lab to lab and must come from your own report.