Girls are asked to wear shawls in church which someone told me that was because Holy Mary wore it. But isn’t this an old tradition? We do not see this followed in other countries?

I hope the issue is about women covering their heads with a veil in prayer. The tradition of women having to cover their head in the Church came about as a result of the exhortation of St. Paul in 1 Cor 11:2-16 and not as you mentioned in the question. 

In the Church, as late as in the beginning of the 20th century, this tradition is generally seen to be followed. Code of canon law (1917) instructed that ‘woman shall have a covered head and be modestly dressed, especially when they approach the table of the Lord’. In 1970, a document issued by the Congregation for the Doctrine of faith stated that ‘It must be noted that these ordinances, probably inspired by the customs of the period, concern scarcely more than disciplinary practices of minor importance, such as the obligation imposed upon women to wear a veil on their head (1 Cor. 11:2-16); such requirements no longer have a normative value’. This mandate of 1917 is seen removed from the extant Canon Law that was published in 1983. So as of now, it is not mandatory for women to cover their heads during the Holy Mass in Latin Rite. But many do. 

Covering the head originated from Judaic cultural customs as well as early Christian tradition. It was embraced as Catholic tradition for the same reasons. However, the significance of using the veil has changed from the cultural tradition from where it began. Nowadays, the use of the veil is considered a visible act of modesty and humility. A veil is not worn out of guilt, or as an act of subservience, or out of shame for feminine beauty, but rather as an expression of reverence and surrender to God’s will.

Women covering their head in church, especially during Holy Mass was and still is a beautiful and dignified practice. Eastern Catholic Churches still follow this tradition and encourages it. If, in your heart, you desire to joyfully adhere to it, go ahead, knowing that you are outwardly expressing the reverence you have for Christ in your heart through this act. If you are uncomfortable, that’s just fine. Either way, always know that you are His darling child and the Father is so glad that you came to talk with Him.