I had a blood test to check my thyroid and was put on 50mg of Synthroid. Recently, after another test, the doctor said the  problem had worsened and increased the dose to 75mg. Should I be worried? 

No, you should not be worried, you should be proactive and tackle the root of your worry.

You have an ongoing thyroid condition that has shown up in a blood test and is currently being treated. That the doctor has increased your dose of Synthroid by half (from 50mg to 75mg) indicates that the conditioning is not improving. You should return to your doctor and ask her answer the following questions fully and so that you understand them completely:

1. Exactly what is my condition and how did I come to have it?

2. Is this a condition that will progressively worsen as I get older? At what rate?

3. If my condition does worsen, what symptoms can I expect to experience?

4. Drugs aside, is there anything I can do to alleviate the condition - i.e. Lifestyle changes?

5. Is it helpful for me to worry? I suspect your doctor's answer to this will be 'No.'

In the meantime, you can read about the medication you are taking here.