Yes, the hypothyroidism is due to Hashi.
Hard to know if any developmental delay is due to sub-optimal treatment of hypothyroidism during pregnancy.
If the thyroid treatment is optimal (TSH around 1) and there is still depression, anti-depressants may be helpful.
You might really benefit from adding Cytomel to your levothyroxine (or switching over to Armour.) I have Hashi's, which is likely what you have. I really struggled with depression while on Synthroid. Was switched to Armour and after a short time, depression resolved. (I didn't need to take any anti-depressants.)
Hi. I was depressed too after birth of my 2nd son and turned out due to Hashimoto's. I did not get any relief whatsoever from T4 only meds. When I began T3 (60mcg)/T4 (50 mcg) combo all the depression, anxiety etc went away completely.
My son was delayed compared to my daughter. However, I have had them both tested and son not Hashi's but daughter is with extremely high abs.
If you are concerned, maybe have them checked - it can only assist with early identification. I wish I'd been diagnosed earlier and had daughter diagnosed earlier as she now has many symptoms at 13yo.