You have not give the Rashi of your son.
Any way the following are few basic principles.
The Guru should be transiting over 2, 5, 7, 9 or 11th house from the Janma Rashi of your son. Currently it is in Kumbham. In June it would be transiting to Meena. The Same should be the case with your janma rashi also. Since your rashi is makaram, Guru in Kumbham is good time for you to give Gayatri to your son i.e, 2nd house from Makaram. Rememer, in no case, the Guru should be in 8th house from that your son's janma rashi. And since, your boy's star is krittika, he should be either in Mesha or Vrishabha. If he is Mesha rashi, you can perform his upanayamam in the month of April, when Guru is Kumbha (i.e, 11th house from mesha). If he is Vrishabha rashi you can perform in the month of June. This is preferable to you, I guess. Guru in 10th house from janmarashi is also favourable.
Next, the following are very important.
The eighth house from the Muhurtha lagna (the time of performing upnayamam) should be vacant. This is Ashthmasuddhi.
The placement of Guru from the muhurtha lagna. Guru can be in lagna or It should be placed in Kendras i.e, 4th house, 7th house or 10th house from the lagna. These houses can be occupied by benefic planets like Sukra and Chandra also. Budha can be considered as he is neither benefic nor malefic.
Malefic planets i.e, Kuja, Ravi and Sani should preferably placed in 3rd, 6th and 11 houses from lagna. You can ignore the shadow planets like Rahu and Ketu in either case. If Ravi is 11th house, they say, all the negative effects are nullified. So, if you can have karkataka lagna in the first week of June, Ravi would be in the 11 house.
9th house should not be occupied by Ravi, KUja, Rahu. Chandra should not be 2, 4,6, and 12. Budha should not be in 12th house.
Next, since your star and his star fall in the same group, you can perform the upanayanam on any day having the stars :Rohini, Hastha, Anuradha, uttarabhadra. You can also consider Ashvini, Pushyami, Swati, Shravana, Shatabhisha.
Upnayam should be performed only in the forenoon.
If your boy is vrishabha raashi, then 15th june, karkataka lagnam would be suitable, I guess. As benefics are in lagna i.e, Sukra and Chandra. Chandra is in his favourable position. Malefic Sani in third house, Ravi in 11th house, which is very desirable. THe eighth house is empty i.e, Ashtamasudhdhi. The star pushyami is favourable to both of you. While the benefics sukra and chandra appear to be bonded, the malefic ravi has no yuthi with budha.