Belinda,
To add to Jane's Post, attached is a parish record of a Martin Harrison being baptised in Tulla in August 1835. Parents: James Harrison and Mary Balton. The address is not clear.
According to Surnames of Ireland by Dr. Edward MacLysaght, the surname "Bolton" is in Ireland since mediaeval times. It is derived from an English place name. It is fairly fairly numerous in all provinces.
In County Clare it has become "Balton".
Tulla parish recordsd are from 1819, so it is unlikely that you will find any birth record for James Harrison. They can be accessed at catholicparishregisters@nli.ie - National Library
There is a record of a William Harrison in Betham's Abstracts which appears to be Garruaugh, Co. Clare for 1791 which may refer to Tulla parish.
Credits: www.findmypast.ie - Subscription site
Regards,