All three phrases introduce your view, but they are not the same. I think = the everyday, neutral choice; it sounds a little soft and is best for casual talk. I believe = stronger and more formal; it shows you feel sure. In my opinion = clearly marks the whole idea as your personal view and fits discussions or writing. Start your sentence with just ONE of them. To say the same as someone else, use I agree — it is a verb, so say I agree, never "I am agree".
Giving your opinion
In my opinion — In my opinion, this museum is interesting.
I think — I think it is a good plan.
I believe — I believe we should wait.
I agree — I agree with you completely.
Not "In my opinion I think this is the best plan." — say "In my opinion, this is the best plan.". Use only ONE opinion phrase to start a sentence. Stacking In my opinion and I think together sounds wrong.
Try it: Mei: What do you think of this museum? Lars: ___ it is really interesting. Lars wants to give his opinion. Which fits best? (In my opinion, / afraid of / proud of) Answer: In my opinion, — In my opinion introduces what you think, which fits. Afraid of and proud of both describe feelings, so neither one introduces an opinion.
Talking about feelings
Use these to say how you feel. interested in something = you want to know more about it. afraid of something = it scares you, usually a real danger. proud of something = you feel good because you did it well. nervous (about) something = you feel worried just before something hard. Watch the difference: afraid of is fear of something dangerous, while nervous about is worry before an event like an exam. Three words describe the THING, not you: something exciting makes you excited, something frustrating makes you annoyed because you cannot do it, and something moving makes you feel emotional, often close to tears.
interested in — I'm interested in modern art.
afraid of — I'm afraid of spiders.
proud of — I'm proud of my work.
nervous — I'm nervous about the exam.
exciting — The concert was so exciting!
frustrating — This puzzle is frustrating — I can't solve it.
moving — That story was so moving. I cried at the end.
Not "I'm afraid of my exam tomorrow." — say "I'm nervous about my exam tomorrow.". An exam is not dangerous, so use nervous about for worry before an event. Save afraid of for real fears like spiders or heights.
Try it: Camila: You finished the whole project by yourself! Farid: Yes, I'm ___ my work. Farid did a good job and feels good about it. Which fits? (proud of / afraid of / nervous about) Answer: proud of — Proud of describes feeling good about something you did well, which fits. Afraid of is about fear and nervous about is about worry, so neither one shows a good feeling about your own work.