Should you see a Celiac Specialist

I'm presuming when you say your gastrologist told you this, that you have had an endoscopy to confirm your diagnosis(?).  Usually, you get a blood test first, then an endoscopy. Once diagnosed with coeliac disease you must cut out all gluten from your diet.  It is not unusual for you to continue to have symptoms for sometime. You will not heal overnight, it may also depend on how long you have had undiagnosed coeliac disease, if you've had it for a considerable length of time, it's going to take longer to recover. No one is the same though, and everyone's symptoms are different. 

I found that following going on to a gluten free diet I started to improve, but once a week my symptoms would 'peak' and couldn't keep my food down, then I'd be okay After about a week the same thing would happen again - this continued for about 6 weeks. Then slowly, but surely, my other niggling (more minor) symptoms started to abate.  Including my thyroid disorder, and I take less medication for it than I did previously.

To answer your question: usually you will have another endoscopy about a year later, to check that your gut is healing and probably you will be seen on a yearly basis to discuss any problems and to do blood tests.  You may also be offered a DEXA scan, to check your bones for signs of osteoporosis, they usually carry them out every few years, this may or may not depend on your local health authority and it could depend on what your calcium and vitamin D levels are like.  Personally, I've had undiagnosed coeliacs for quite a long time (more than 30 years) and was in poor state of health. You may not have the same problems.

The other thing you need to bear in mind, is whether you are inadvertently letting gluten into your diet, this will effect your recovery.  You need to be strict with preparation areas and washing surfaces down regularly and having your own pots, pans and utensils to ensure you are not ingesting gluten from anyone else's kitchen equipment.  Don't use things like wooden chopping boards or wooden spoons as they are porous and will absorbe gluten.  Have your own washing up cloths and if possible, your own area in the kitchen for preparing your food.  Also, do not share toasters with people that eat gluten, you need to have your own separate one. It's all about common sense and carefully eliminating all possible risks of cross contamination.  If you are not a member of coeliac uk, I would recommend joining (your first 6 months are free, to help you start on your journey), if possible, continue with the membership as they have an app you can download on your mobile, which helps you when you are shopping for gluten free foods.  They also send you a regular magazine and have a telephone helpline, etc.

Also, in the first year, you are recommended not to eat oats (that includes oats which have been prepared in gluten free conditions) because the protein in oats can have the same effect on the lining of the gut as gluten - although this only usually effects about 1% of the population. After the first year, you can then try oats but only those classed as gluten free.  

I hope that this has helped you and that you start to feel better soon.  

You are a few years younger than me and I was originally diagnosed with IBS when I was about 22. It is still fairly early days for you, and I wouldn't get too despondent. Your gut still has a lot of healing to do. You will probably get yearly blood tests done to keep an eye on things. I see my specialist once a year. 

As your gut heals, your thyroid medication will be more absorbed into your gut/bowel and so you might find that they need to lower the dosage of your medication as you continue to heal.  (Your usual thyroid blood tests will reflect this.  That is what happened to me.  Bit by bit, things should gradually improve. Good luck!