If I had asthma as a child, should I be concerned about my 10 month old developing it?

Maybe. Many infants have predisposing factors such as family history as well as a history of atopy or cows milk allergy. Some babies wheeze because they have reflux, others develop chronic wheezing problems secondary to infections such as rsv. Do not forget environmental factors such as second hand smoke and exposure to fumes. Yet it does not mean your child will be an asthmatic.
Possibe not Definate. Asthma is varible in the iindividual & family groupings. There appears to be a toddlers wheezing that tracks in asthma families and most grow out of by school age.Often triggered by infection, this can be troublesome. There is some overlap in pattern with more severe asthma, often leading to ICU care by a year in males, females seem to do it by 4. Discuss your concerns with your doctor to be sure.
Don't be worried yet. Asthma and allergies run in some families, but if an older baby has been well so far, one need not worry about his getting asthma. Try to avoid things that may start wheezing, such as catching RSV bronchiolitis, breathing second-hand smoke, or playing in a moldy/dusty place (such as on old carpets). If he starts wheezing, then one can worry a bit. Some kids don't get asthma even if mom/dad has it.