Please, try to talk with your doctor.
You mustn't stop taking methyldopa without consulting your doctor, because abruptly stopping methyldopa may increase blood pressure and cause unwanted side effects.

Yes, upset stomach and vomiting are side effects of methyldopa.
Methyldopa has not been studied in pregnant women in the first and second trimesters (the first 6 months of pregnancy). Studies in pregnant women during the third trimester (the last 3 months of pregnancy) have not shown that methyldopa causes birth defects or other problems.
However, every medicine taken during first trimester of pregnancy has potential risks for growth and development of the fetus.

When did you discover that you have problems with your blood pressure for the first time?

I stopped talking methyldopa altogether and I feel alot better. My blood pressure spikes sometimes and gets high but mostly it stays about 125/85. I don't think that's too horrible but my doctor insisted I take this nasty medication. I am a very holistic person, I deal with health problems naturally and I am not the type to just take a pill because my doctor said so. I researched it and was appalled that this medication hasn't been studied for use in the first and second trimester. My baby and I am not a guinea pig for my doctor to experiment with. She assured me methyldopa is safe but obviously she has no idea what she is talking about. How can she know if there haven't been studies? I am glad I only took it for a few weeks. I am worried about any harm it has done to my baby.

To answer your question, I discovered I had high blood pressure years ago. It runs in my family, every person has it including my mom, dad, granparents, and aunts.

I'm happy that you are feeling lot better.
I'm sure I'll act the same if I was in your situation ( cutting off the medicine).
The use of medicine is reasonable when it's more beneficial than harmful (but, you need firm facts for that)
Blood pressure range of 100/70 - 125/85 is generally considered to be a normal, so, keep tracking your blood pressure readings (you can start a diary) and practice good diet, exercise, lower your salt intake and weight.

Since I changed my diet, my bp has been alot better. I try to eat alot more healthy now, no junkfood, pizza, that kind of stuff. I got a membership at the YMCA here so I will start swimming at least 3 times a week. Hopefully that will help too. The things that gets me is that my dr. told me not to take garlic supplements which have always helped me with high bp. She said the reason I shouldn't take them is because no studies have been done on how it will effect the pregnancy. Then she prescribes me something that no studies have been done on either. I would much rather take something natural that has always helped me than some weird chemical concoction. I'm going to ask her these question at my next appt. I have read that methydopa is generally ok to take during pregnancy, but how does anyone know if no studies have been done on it? It makes no sense.

Garlic supplements or large amounts of garlic should be avoided during pregnancy due to a possible increased risk of bleeding. In addition, early animal studies suggest that garlic may cause contraction of the uterus. Many tinctures contain high levels of alcohol, and should be avoided during pregnancy.
You can continue to use garlic in amounts usually eaten in food.
Its use can cause only small reductions in blood pressure (<10mmHg).